Matrix multiplication is not commutative: A x B is generally not equal to B x A.
Enter valid numbers in every cell.
This matrix is not invertible: its determinant is 0.
Matrix operations for A-level Further Maths
Matrices sit on the A-level Further Maths syllabus, where students calculate determinants, find inverses, and multiply 2x2 and 3x3 matrices by hand as part of the pure core content. This calculator covers the same ground: pick a size, choose an operation, and the result appears as a matrix grid rather than a single number, so you can check your own working line by line.
Determinant and inverse formulae
| Operation | 2x2 formula |
|---|---|
| Determinant | det(A) = ad - bc, for A = [[a,b],[c,d]] |
| Inverse | A-1 = (1 / det(A)) x [[d,-b],[-c,a]] |
For a 3x3 matrix, the calculator expands the determinant by cofactors along the first row, then builds the inverse from the adjugate matrix (the transpose of the cofactor matrix) divided by the determinant, the standard method covered in Further Maths textbooks.
Where this tool falls short
This calculator only handles square matrices up to 3x3. It does not support rectangular matrices, matrices larger than 3x3, eigenvalues, eigenvectors, or reducing a system of equations to row echelon form. When the determinant is 0, the matrix has no inverse and the tool says so plainly instead of dividing by zero.
A mistake worth avoiding
Matrix multiplication is not commutative, so A times B is generally not the same as B times A, and mixing up the order is one of the most common errors in exam working. Pair this tool with the Quadratic Equation Solver for other algebra, or the Scientific Calculator for general working.