Matrix subtraction calculator
Type two matrices of the same size, one row per line, and get A − B.
One row per line, numbers separated by spaces. Fractions such as 1/2 are allowed.
Fill in the fields; the answer appears here straight away.
How it's worked out
How it works
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Enter the values
Type the numbers or the formula. Decimals may use a point or a comma. No idea? Click Fill in an example.
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Instant answer
The answer appears as you type, with the most important intermediate values.
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See the working
Under "How it's worked out" you see the steps, handy for checking your own calculation.
How matrices are subtracted
Subtract the numbers in the same position. For A = [[5, 6], [7, 8]] and B = [[1, 2], [3, 4]], A − B = [[4, 4], [4, 4]]. Note that A − B is not the same as B − A: every sign flips.
Both matrices need the same size. Fractions are allowed and the result is exact. To add, use the matrix addition calculator.
A 2 × 3 example
| A | B | A − B |
|---|---|---|
| 1 0 2 | 2 5 −2 | −1 −5 4 |
| 3 −1 4 | 0 1 1 | 3 −2 3 |
Each entry is the difference of the entries in the same position: 1 − 2 = −1, 0 − 5 = −5, 2 − (−2) = 4.
Differences between data sets
Subtracting is how you compare two tables of the same shape: this year's figures minus last year's, a measured grid minus a prediction, or one image minus another to see what changed. Positive entries are increases and negative entries decreases, so the signs carry meaning. Combine with matrix addition to rebuild the original: (A − B) + B = A.
Next steps
Whether a matrix can be inverted depends on its determinant, which you can calculate with the determinant calculator.
Frequently asked questions
Is A − B the same as B − A?
No. Swapping them flips every sign: if A − B has the entry 4, then B − A has −4 in the same position.
What size must the matrices be?
The same. Both need the same number of rows and columns, and the calculator says so when they differ.
How do I subtract a matrix from itself?
You get the zero matrix, with only zeros, because every entry minus itself is 0.
Is subtracting the same as adding the negative?
Yes. A − B = A + (−B), where −B has every entry of B with its sign changed.