The inverse of A is the matrix A⁻¹ such that AA⁻¹ = I. Like 1/x for matrices.
Edit the matrix
A
→
A⁻¹ = (1/det)·adj(A)
0.4
-0.1
-0.2
0.3
det = 10
Edit the matrix above so ad − bc = 0 (e.g. [1 2; 2 4]) and the inverse vanishes — that matrix is singular. Only matrices with nonzero determinant can be inverted.
Your turn
Find the inverse of [2 1; 1 1].
Solving Ax = b becomes x = A⁻¹b — the matrix version of dividing both sides. It's how a system of equations gets handed to a computer.
2×2 inverse
If determinant = 0, the matrix has no inverse — it's singular.