Matrix Addition Calculator
Add two matrices of identical dimensions and see the element-wise result instantly.
How it works
- 1Choose the number of rows and columns (1–4). Both matrices resize together so their dimensions always match.
- 2Fill in the cells of Matrix A and Matrix B. Each cell accepts any real number.
- 3The result matrix A + B is computed instantly — each entry (i, j) equals A[i][j] + B[i][j].
Use cases
- Combining transformation matrices in computer graphics or robotics.
- Summing data tables in statistics, economics, or engineering analysis.
- Checking hand-computed matrix addition homework step by step.
Frequently asked questions
Why must A and B have the same dimensions?
Matrix addition is defined only for matrices of identical size because each element of A is paired with the element in the exact same position in B. If the dimensions differ, there is no counterpart for every cell, so the operation is undefined.
Is matrix addition commutative?
Yes — A + B = B + A for all matrices of the same dimensions. Unlike matrix multiplication, addition is both commutative and associative.
What is the zero matrix in addition?
The zero matrix (all entries equal to 0) acts as the additive identity: A + 0 = A. Any matrix added to the zero matrix of the same size returns the original matrix unchanged.
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