Matrix Reasoning Questions: 3x3 Grid Practice With Answers
A matrix reasoning question shows a 3x3 grid of figures with one cell missing, and you pick the option that completes it. The fastest reliable method is to check rows first, then columns, testing a short list of rules: counting, distribution, progression, rotation, overlay and subtraction. Below you will find each rule explained, a worked example and eight practice grids described in words, with answers.
How a Matrix Question Is Built
A typical item has:
- Eight filled cells containing shapes, lines, dots or symbols
- One empty cell, often bottom-right but sometimes in the middle or a corner
- Four to eight answer options, of which exactly one fits every rule
Test makers build the grid by picking one to three variables (for example shape, shading and number) and assigning each a rule that runs across rows, down columns or both. Wrong options are designed to satisfy some rules but not all. That is why the trap answer usually looks almost right: it was built to.
Matrix items are the backbone of Raven's Progressive Matrices and the Wechsler Matrix Reasoning subtest, and they appear in most employer abstract reasoning tests from SHL, Korn Ferry, Aon and Saville. For background on why IQ tests rely on them, see abstract reasoning in IQ tests.
The Seven Rules Behind Most 3x3 Grids
| Rule | What happens | How to spot it |
|---|---|---|
| Distribution of three | Each row and column contains each of three values once (like a Sudoku) | The same three shapes or fills keep reappearing in different orders |
| Progression | A value increases or decreases steadily along a row or column | Counts or sizes climb 1, 2, 3 or shrink large, medium, small |
| Arithmetic | Cell 3 equals cell 1 plus (or minus) cell 2 | Count elements; the third cell matches a sum or difference |
| Rotation | An element turns by a fixed angle each step | Track one distinctive corner or tip |
| Reflection | An element is mirrored between cells | Compare left-right or top-bottom orientation |
| Overlay | Cell 3 is cells 1 and 2 placed on top of each other, sometimes with shared lines removed | Cell 3 looks busier than cells 1 and 2 |
| Subtraction | Cell 3 keeps only what is in cell 1 and not in cell 2 | Cell 3 looks emptier than cell 1 |
Most grids use one of these on its own; harder ones layer two or three, often one rule for the outer shape and another for an inner detail. For a deeper look at each pattern type, see our guide to abstract reasoning patterns explained.
A Five-Step Method
- Name the variables. Before looking for rules, list what differs between cells: shape, fill, number, size, orientation, position.
- Read the complete rows. Rows 1 and 2 are full, so they show you the rule. Apply it to row 3.
- Confirm with the columns. If the column rule agrees, you are almost certainly right. If it conflicts, you have the wrong rule.
- Predict before looking at the options. Describe the missing cell in words first, then find it. This stops attractive distractors from steering you.
- Eliminate if stuck. Strike out any option that breaks a rule you are sure of. Often only one or two options survive.
Worked Example
Row 1: one circle, two circles, three circles. Row 2: two squares, three squares, four squares. Row 3: three triangles, four triangles, missing.
Variables: shape and number. Rows: each row keeps one shape and adds one element per cell. Columns: the count also rises by one going down (1, 2, 3 in column 1), so column 3 runs 3, 4, missing. Prediction: five triangles. Both directions agree. An option showing five squares is the trap: right number, wrong shape for row 3.
Practice Grids With Answers
Cells are described left to right. Sketch the grid if it helps.
Question 1
Row 1: 1 star, 2 stars, 3 stars. Row 2: 2 hearts, 3 hearts, 4 hearts. Row 3: 3 crosses, 4 crosses, missing.
A) 4 crosses B) 5 crosses C) 5 hearts D) 6 crosses
Answer: B. Each row keeps its symbol and adds one per cell, and each column also rises by one. Row 3 needs 5 crosses.
Question 2
Each cell holds one arrow. Row 1: up, right, down. Row 2: right, down, left. Row 3: down, left, missing.
A) Up B) Right C) Down D) Left
Answer: A. The arrow turns 90 degrees clockwise from one cell to the next in each row (and in each column). After left comes up.
Question 3
Column 1 holds circles, column 2 squares, column 3 pentagons. In each column the top shape is white, the middle grey and the bottom black. The missing cell is row 2, column 3.
A) White pentagon B) Grey pentagon C) Black pentagon D) Grey square
Answer: B. Column 3 contains pentagons, and the middle row is always grey.
Question 4
Each cell contains a single dot that is small, medium or large and sits at the top, middle or bottom of the cell. Row 1: small at top, medium in middle, large at bottom. Row 2: medium at bottom, large at top, small in middle. Row 3: large in middle, small at bottom, missing.
A) Medium at top B) Medium at bottom C) Large at top D) Small at top
Answer: A. Every row and column contains each size once and each position once. Row 3 is missing medium and top. Column 3 (large bottom, small middle, medium top) confirms it.
Question 5
Each cell is a square frame with lines inside. In each row, cell 3 combines the lines of cells 1 and 2. Row 1: a vertical line; a horizontal line; a cross (vertical plus horizontal). Row 2: a diagonal from top-left to bottom-right; a diagonal from top-right to bottom-left; both diagonals (an X). Row 3: a vertical line; a diagonal from top-left to bottom-right; missing.
A) A vertical line and a top-left to bottom-right diagonal B) A vertical line and a top-right to bottom-left diagonal C) A cross and an X together D) A top-left to bottom-right diagonal only
Answer: A. Cell 3 is the overlay of cells 1 and 2, so it shows exactly the vertical line and the top-left to bottom-right diagonal.
Question 6
Each cell contains a group of small symbols. In each row, cell 3 shows what is in cell 1 but not in cell 2. Row 1: circle, square, triangle; square; circle, triangle. Row 2: star, heart, circle; star, circle; heart. Row 3: square, star, heart, triangle; heart, square; missing.
A) Star and triangle B) Square and heart C) Star, heart and triangle D) Triangle only
Answer: A. Removing the heart and square from cell 1 leaves star and triangle. Option B is what was removed, the classic reversal trap.
Question 7
The missing cell is in the centre (row 2, column 2). Row 1: white triangle, black square, white pentagon. Row 2: black square, missing, black hexagon. Row 3: white pentagon, black hexagon, white heptagon.
A) White pentagon B) Black pentagon C) White square D) Black hexagon
Answer: A. Moving one cell right or one cell down adds a side, so the centre has one more side than the square above it and one fewer than the hexagon beside it: a pentagon. Shading follows a checkerboard, and the centre matches the corners, so it is white. The diagonal from top-right to bottom-left (pentagon, centre, pentagon) confirms the shape.
Question 8
Each cell shows an outer shape with a smaller shape inside it. Row 1: circle containing a square; square containing a triangle; triangle containing a circle. Row 2: square containing a star; star containing a circle; circle containing a square. Row 3: triangle containing a heart; heart containing a star; missing.
A) Star containing a triangle B) Star containing a heart C) Triangle containing a star D) Heart containing a triangle
Answer: A. Two rules work together. The inner shape of each cell becomes the outer shape of the next cell, so cell 3 is a star. The inner shape of cell 3 is the outer shape of cell 1 in the same row (circle in row 1, square in row 2), so in row 3 it is a triangle. Option B fails because the heart would repeat an inner shape already used in that row.
Common Mistakes
Stopping after one row. A rule that fits row 1 but not row 2 is not the rule. Always test it on both complete rows.
Ignoring the second variable. In Question 7, many people find the shape and forget the shading. When options differ only in fill or size, that variable carries a rule too.
Confusing overlay and subtraction. If cell 3 has more elements than cell 1, think overlay. If it has fewer, think subtraction or cancellation.
Choosing the first plausible option. Distractors are designed to satisfy one rule. Predict the answer before reading the options.
Time Strategy for Matrix Tests
Most matrix tests give 45 to 90 seconds per grid. A workable split:
- 0 to 15 seconds: name the variables and read row 1.
- 15 to 40 seconds: form the rule, check row 2 and a column.
- 40 to 60 seconds: predict and select, or eliminate.
- Over 75 seconds: pick the best remaining option, flag it if the test allows, and move on.
Easy grids should take 20 to 30 seconds, which buys time for the two or three hard ones at the end. More shortcuts are in solving matrix reasoning quickly.
A Ten-Day Practice Plan
| Days | Focus |
|---|---|
| 1 to 2 | Distribution and progression grids, untimed. Write the rule in one sentence. |
| 3 to 4 | Arithmetic, overlay and subtraction grids. |
| 5 to 6 | Rotation and reflection; practise tracking one distinctive feature. |
| 7 to 8 | Two-rule grids and grids with the gap in the middle or a corner. |
| 9 to 10 | Timed mixed sets of 15 grids at your target test's pace, then review every miss. |
When a grid has a gap somewhere other than the end, the approach is the same as for missing shape questions: use the cells on both sides of the gap as a double check. For timed practice in the real format, try the abstract reasoning test.
Frequently Asked Questions
How long do I have per matrix question?
Employer tests usually allow 45 to 90 seconds per matrix item, depending on the publisher and difficulty. Practise at about 60 seconds per grid, then tighten that to the exact budget of your target test once you know it.
Can the missing cell be anywhere?
Yes. The bottom-right cell is the most common gap, but tests also remove a middle or corner cell. The rule still runs through the full row and column, so read both directions and check that your answer fits each one.
What if two options seem to fit?
Go back to the grid and look for a second variable you have not checked, such as shading, size or the number of elements. In a well-built matrix only one option satisfies every rule, so the difference between the two candidates is usually the rule you missed.
Are matrix reasoning questions the same as Raven's matrices?
Raven's Progressive Matrices popularised the format, and most employer matrix items follow the same logic. Employer versions are usually more strictly timed and sometimes use a 2x2 or 3x3 grid with five or more answer options.
Which rule should I check first?
Start with the quickest checks: count the elements in each cell, then look at shading, then rotation. Distribution rules, where each row holds one of each item, are among the most common in 3x3 grids and are easy to spot once you look for them.