Quick start
- Choose 2x2 or 3x3.
- Choose the operation you want.
- Enter Matrix A. Enter Matrix B too for add, subtract, and multiply.
- Press Calculate matrix, then check the result, steps, examples, and recent answers.
Best uses
Use this page when the problem is about small square matrices and you want to check the answer without losing the row and column logic.
- Check 2x2 and 3x3 matrix addition or subtraction before homework goes in.
- Multiply square matrices and see the row-by-column rule instead of just the answer.
- Find a 2x2 determinant with ad - bc or a 3x3 determinant with expansion by minors.
- Transpose a matrix when rows and columns need to switch places.
Fast 2x2 checks
For addition, match the same position in each matrix. [[1,2],[3,4]] plus [[5,6],[7,8]] becomes [[6,8],[10,12]]. Nothing moves around.
For a 2x2 determinant, use ad - bc. Matrix [[3,4],[2,5]] gives 3x5 - 4x2 = 7. If you get a different number, check the diagonal order first.
Matrix multiplication order
Matrix multiplication uses rows from Matrix A and columns from Matrix B. That is why A x B can be different from B x A.
Example: [[1,2],[3,4]] x [[2,0],[1,2]] gives [[4,4],[10,8]]. The top-left answer is 1x2 + 2x1 = 4.
Determinant and transpose
A determinant is one number from a square matrix. A 3x3 determinant needs more steps, so use the calculator output as a check while you study the expansion.
Transpose swaps rows and columns. Entry row 1, column 2 becomes row 2, column 1. This page keeps the grid at 2x2 and 3x3 so it stays readable on a phone.
Mistakes to check first
Addition and subtraction need the same matrix size. If the problem mixes sizes, the operation is not defined.
Do not flip multiplication order unless your teacher or source says to. Matrix A times Matrix B is a different question from Matrix B times Matrix A.
Worked examples for Matrix Calculator
[[4,4],[10,8]] because row 1 x column 1 is 1x2 + 2x1 = 4
[[6,8],[10,12]] by adding matching spots
7 because 3x5 - 4x2 = 15 - 8
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FAQ in plain language
What matrix operations are supported?
The Matrix Calculator supports addition, subtraction, multiplication, determinant, and transpose for 2x2 and 3x3 square matrices.
When can I add or subtract two matrices?
The two matrices need the same size. A 2x2 can add to another 2x2, and a 3x3 can add to another 3x3. Each answer spot comes from the matching spot in Matrix A and Matrix B.
What do the main Matrix Calculator inputs mean?
Choose 2x2 or 3x3, then enter each value in its row and column in Matrix A. Add, Subtract, and Multiply also use the matching-size Matrix B grid. Determinant and Transpose only use Matrix A. Entries can be positive, negative, whole, or decimal numbers.
How should I read the Matrix Calculator answer?
Add, Subtract, Multiply, and Transpose return a matrix with rows and columns in square brackets. Determinant returns a single number. Check Operation, Size, and Uses Matrix B below the answer, then read Steps to follow the selected operation.
What should I double-check before trusting the Matrix Calculator?
Check the selected size and operation, then check every row and column position and negative sign. Keep Matrix A and Matrix B in the intended order for multiplication because A x B can differ from B x A. Press Calculate matrix after changing an entry before copying the answer.
Does order matter for matrix multiplication?
Yes. Matrix multiplication is order-sensitive. A x B can be different from B x A because each answer entry uses a row from the first matrix and a column from the second.
What is a determinant?
A determinant is a single value calculated from a square matrix. For a 2x2 matrix [[a,b],[c,d]], the determinant is ad - bc.
Sources
Use these if you want to compare the formula, inputs, or limits with a trusted outside explanation.
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Keep exploring
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- Free calculator resourcesStart here when you are not sure which calculator page fits.
Privacy and copying results
Recent answers stay visible only while you work in the current browser tab. They are not sent to a server.
Use Copy answer when you want to save the inputs and result in notes, homework, a message, or a project list. Check the units, labels, and limits before copying.