Matrix Addition Calculator

Use our free matrix addition calculator to add two matrices of the same dimensions. Shows element-wise sums and the commutative property.

Math

Matrix A

Matrix B

Formula

Matrix addition adds corresponding elements: (A+B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ. Both matrices must have the same dimensions. Matrix addition is commutative and associative.

(A + B)ᵢⱼ = Aᵢⱼ + Bᵢⱼ

Percentage: The percentage value you want to apply

Number: The original number or value

Result: The calculated result

How It Works

1Enter Matrix A (rows separated by ;, columns by ,).
2Enter Matrix B (same dimensions).
3Click Calculate to add element-wise.

Examples

Add 2×2 matrices

1.[[1+5,2+6],[3+7,4+8]] = [[6,8],[10,12]]

Result: 6

Add 1×3 vectors

1.[10+1, 20+2, 30+3] = [11, 22, 33]

Result: 11

Frequently Asked Questions

When they have the exact same dimensions.

Yes, A + B = B + A.

Yes, (A + B) + C = A + (B + C).

A matrix of all zeros that acts as the additive identity.

This computes matrix + matrix, not scalar + matrix.

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CalculateMe Team

Last updated: 2026-07-14

Matrix Addition Calculator

Formula

How It Works

Examples

Add 2×2 matrices

Add 1×3 vectors

Frequently Asked Questions

When can I add matrices?

Is addition commutative?

Is addition associative?

What is the zero matrix?

What about scalar addition?

Related Calculators

Matrix Addition Calculator

Formula

How It Works

Examples

Add 2×2 matrices

Add 1×3 vectors

Frequently Asked Questions

When can I add matrices?

Is addition commutative?

Is addition associative?

What is the zero matrix?

What about scalar addition?

Related Calculators