Matrix Addition & Subtraction Calculator

Add or subtract two matrices element by element. Every position is shown as A[i][j] ± B[i][j] with the full working.

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Rows

Columns

Matrix A

Matrix B

Result

Add or subtract two matrices of the same size, element by element, with the calculation for every single position shown in full.

How It Works

How Matrix Addition & Subtraction Calculator Works

Matrix addition and subtraction both work entry by entry using the rule C[i][j] = A[i][j] ± B[i][j] — each position in the result comes only from the matching position in A and B, with no cross-multiplication or combining of other entries involved.

Because of this position-by-position rule, both matrices must have exactly the same number of rows and the same number of columns; there is no way to add or subtract matrices of different shapes.

Switching between the Addition and Subtraction modes instantly recomputes every cell of the result using the same two input matrices, letting you compare A+B against A−B side by side.

Worked Example

See It In Action

For A = [[4,1],[2,7]] and B = [[3,5],[6,0]]: adding entry by entry gives A + B = [[7,6],[8,7]] (e.g. top-left: 4 + 3 = 7), while subtracting gives A − B = [[1,-4],[-4,7]] (top-right: 1 − 5 = −4). Every position is computed completely independently of the others.

Real-World Use Cases

Who Uses Matrix Addition & Subtraction Calculator and Why

Combining two data matrices representing the same categories — like two months of sales figures broken out by region and product — entry by entry.
Computing the difference between two states of the same system, such as before-and-after measurements arranged in matrix form.
Checking a small homework addition or subtraction problem entry by entry against the full worked-out result.
Comparing A + B and A − B side by side using the exact same pair of input matrices.

Common Mistakes

Mistakes to Avoid

Entering two matrices of different sizes — addition and subtraction require identical dimensions, since each result entry only comes from the matching position in A and B.
Assuming subtraction is commutative like addition — A − B does not equal B − A in general, even though A + B always equals B + A.
Confusing this position-by-position operation with matrix multiplication, which instead combines entire rows and columns using dot products and has completely different size requirements.

Pro Tips

Tips for Best Results

Double-check both matrices share the same number of rows and columns before entering values, since there's no way to add or subtract mismatched shapes.
Switch between the Addition and Subtraction modes on the same inputs to compare A + B against A − B without re-entering either matrix.

Troubleshooting

Fixing Common Problems

The calculator won't combine my two matrices. — Confirm both matrices have exactly the same number of rows and the same number of columns — addition and subtraction are undefined for mismatched shapes.

My subtraction result doesn't match what I expected from adding. — Remember subtraction isn't commutative — A − B and B − A give different (sign-flipped) results, unlike addition.

Glossary

Terms Explained

Element-wise operation: A calculation applied independently to each matching position in two matrices, as opposed to one combining whole rows and columns.

Commutative: A property where swapping the order of an operation's inputs doesn't change the result — true for matrix addition, but not for subtraction.

FAQ

Frequently Asked Questions

Why must both matrices be the same size to add or subtract them?

Since each result entry is computed only from the matching entries of A and B, every position in one matrix needs a corresponding position in the other — matrices of different dimensions simply have no matching entries to combine.

Is matrix addition commutative — does A+B equal B+A?

Yes — since addition at each position is just ordinary number addition (which is commutative), A + B always equals B + A. Subtraction, however, is not commutative: A − B does not equal B − A in general.

How is this different from matrix multiplication?

Addition and subtraction combine entries at the same position in both matrices, while multiplication combines an entire row of A with an entire column of B using dot products — a completely different operation with different size requirements.

Can I subtract a matrix from a differently-sized one?

No — matrix subtraction, like addition, is only defined when both matrices share identical dimensions, so a 2×3 matrix cannot be subtracted from a 3×2 matrix even though they contain the same number of entries.