2x2 Matrix Calculator
Enter two 2x2 matrices and an operation to find the result, plus each matrix's determinant.
How 2x2 matrix operations work
Matrix addition and subtraction combine corresponding elements directly: each entry in the result is the sum (or difference) of the matching entries in A and B. Matrix multiplication works differently — each entry in the result is a sum of products, following the row-times-column rule.
The determinant of a 2x2 matrix [a b; c d] is calculated as ad − bc. It's a single number that captures important properties of the matrix, including whether it can be inverted (a matrix with determinant 0 has no inverse).
Frequently asked questions
Can you add matrices of different sizes?
No — matrix addition and subtraction require both matrices to have the same dimensions, since each operation combines corresponding positions.
Is matrix multiplication the same as multiplying each element?
No — unlike addition, matrix multiplication uses the row-times-column rule, where each output entry is a sum of products across a row of the first matrix and a column of the second.
What does a determinant of zero mean?
A determinant of zero means the matrix is "singular" — it has no inverse, and the linear transformation it represents collapses the plane onto a line or a point rather than preserving area.