Matrix Reasoning Questions: How to Solve 3x3 Grid Problems
Matrix reasoning questions are among the most common in abstract reasoning tests. You see a 3×3 grid of shapes with one cell missing, and you must choose the correct completion from several options. This article explains how to approach matrix questions systematically and spot the rules quickly.
What Is a Matrix Reasoning Question?
A typical matrix question shows:
- Eight cells filled with shapes, symbols or figures
- One empty cell (often bottom-right, but can be anywhere)
- Four to six options (A, B, C, D, etc.) from which you choose the correct one
The rule that governs the grid may apply across rows, down columns, along diagonals, or in a more complex way. Your job is to find that rule and select the option that fits.
Step-by-Step Approach
Step 1: Scan the whole grid – Don't focus on one cell. Look at all eight filled cells. What elements appear? Shapes, dots, lines, colours?
Step 2: Check rows – Does each row follow a pattern? For example, does a shape rotate 90° as you move left to right? Does the number of elements increase?
Step 3: Check columns – Does each column follow a pattern? Sometimes the rule applies vertically rather than horizontally.
Step 4: Check diagonals – Less common, but some matrices use diagonal rules. Top-left to bottom-right, or top-right to bottom-left.
Step 5: Consider combination rules – Rows might follow one rule (e.g. rotation) and columns another (e.g. colour). Or the rule might be "each row contains one of each type."
Step 6: Eliminate wrong options – Even if you're not 100% sure of the rule, you can often rule out options that clearly violate it. For example, if the rule is "each row has one black and two white shapes," eliminate any option that breaks that.
Common Matrix Rules
Row-wise rotation – Each row shows a shape rotating 90° per cell. The missing cell continues the rotation.
Column-wise progression – Each column has a sequence. The bottom cell completes the sequence for that column.
Distribution rule – Each row (or column) contains one of each type. For example, one circle, one square, one triangle per row. The missing cell gets the type that's not yet in its row.
Addition rule – Moving across or down, elements are added. Row 1 has one shape, row 2 has two, row 3 has three. The missing cell has the right number and type.
Transformation rule – A shape transforms as it moves. It might get larger, change colour, or gain a detail. The missing cell shows the next step in the transformation.
Tips for Speed
Start with the simplest rules – Rotation and reflection are quick to check. Try those first.
Use the options – Look at the options. Do any of them obviously not fit? Eliminate them. Sometimes the difference between options is small—focus on that difference.
Don't overcomplicate – The correct rule is usually straightforward. If you're inventing a complex explanation, you may have missed a simpler one.
Practise under time pressure – Matrix questions often allow 45–60 seconds. Get used to that pace.
Common Mistakes
Assuming the rule from one row – The rule must hold for all rows and columns. Verify before committing.
Ignoring the empty cell's position – The missing cell might be in the middle. The rule still applies—you're completing a row, column or pattern.
Choosing the first plausible option – There may be several options that look right. Make sure your chosen option fits the entire grid, not just one part.
Practice with abstract reasoning questions and the abstract reasoning test.
Frequently Asked Questions
How long do I have per matrix question?
Typically 45–90 seconds, depending on the test. SHL and Korn Ferry often allow around 60 seconds. Practise at that pace.
Can the missing cell be anywhere?
Yes. It's often bottom-right, but it can be in any position. The rule still applies—you're completing the pattern.
What if two options seem to fit?
Re-check the rule. One of them usually violates it when you look at the whole grid. If truly ambiguous, make your best guess and move on.