Matrix Addition Calculator
Add two matrices of any size instantly. Select the matrix dimensions, fill in the entries, and get the result matrix.
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Notes
How Matrix Addition Works
Two matrices can be added only if they have the same dimensions. Each element of the result is the sum of the corresponding elements.
Worked Example
Let A be:
| 1 | 2 |
| 3 | 4 |
Let B be:
| 5 | 6 |
| 7 | 8 |
Result A + B:
| 6 | 8 |
| 10 | 12 |
Properties: addition is commutative (A+B = B+A) and associative ((A+B)+C = A+(B+C)).
Both matrices must be the same size. You cannot add a 2×3 matrix to a 3×2 matrix.
See also
- Matrix Calculations Guide — Addition & Subtraction — In-depth notes on Addition & Subtraction with worked examples
Frequently Asked Questions
Can I add matrices of different sizes?
No. Matrix addition is only defined for matrices with identical dimensions (same number of rows and columns).
Is matrix addition commutative?
Yes. A + B = B + A for any two matrices of the same size.
What is the zero matrix in addition?
Adding the zero matrix (all entries are 0) to any matrix leaves that matrix unchanged: A + 0 = A.