Matrix Calculator (2×2 & 3×3)
Add, subtract and multiply matrices, and find the determinant, inverse and transpose — with working.
Result
How to use
- 1
Pick the size (2 × 2 or 3 × 3) and the operation.
- 2
Type the numbers into matrix A (and B for add, subtract and multiply).
- 3
The answer appears with the determinant and step-by-step working.
Questions
When can two matrices be multiplied?
A × B works when the number of columns of A equals the number of rows of B. For square matrices of the same size it always works — but A × B is usually not equal to B × A.
How do I find the inverse of a 2 × 2 matrix?
For [a b; c d], swap a and d, change the signs of b and c, then divide everything by the determinant ad − bc. If the determinant is 0 the matrix has no inverse (it is singular).
How is a 3 × 3 determinant calculated?
Expand along the first row: a(ei − fh) − b(di − fg) + c(dh − eg), where the matrix is [a b c; d e f; g h i].
About this Matrix tool
Matrix Calculator (2×2 & 3×3) — Add, subtract and multiply matrices, and find the determinant, inverse and transpose — with working. It is one of 200 free tools on namasivayam.in, made by software engineer Namasivayam Vadivelan for everyday use in India.
Everything is calculated instantly in your browser: nothing you type or upload is sent to any server, there is no sign-up, and it works on mobile and desktop. Pick the size (2 × 2 or 3 × 3) and the operation.
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Results are estimates to help you plan. They are not financial, tax or medical advice.