Pick the size of each matrix, enter the values, choose an operation, and get the result instantly — works for 2×2 and 3×3 matrices.
Matrix Calculator
How It’s Calculated
Addition and subtraction combine corresponding entries directly, and only work when both matrices are exactly the same size. Multiplication is different: each entry in the result is the dot product of a row from Matrix A with a column from Matrix B, and it only works when the number of columns in A equals the number of rows in B. This calculator checks that compatibility for you before computing anything.
Worked Example
Multiplying A = [[1,2],[3,4]] by B = [[5,6],[7,8]]: the top-left entry of the result is (1×5) + (2×7) = 19. Work through all four entries the same way — row of A, column of B, multiply and sum — to get the full result [[19,22],[43,50]].
Frequently Asked Questions
Q: Why can’t I add a 2×2 matrix to a 3×3 matrix?
Addition and subtraction only make sense when both matrices have identical dimensions — there’s no mathematically valid way to combine a 2×2 and a 3×3 matrix directly.
Q: Is A × B the same as B × A?
Almost never. Matrix multiplication order matters — reversing the order usually gives a completely different result, or may not even be defined.
This is exactly the operation-order habit Daniel Sir drills into every 2nd PUC batch on Matrices. Read the full Matrices chapter guide →