Check that the matrix is square
Compute the determinant
If the determinant is 0, the inverse does not exist
If the determinant is not 0, proceed to find the inverse
For a 2×2 matrix (begin{bmatrix}a & b \ c & dend{bmatrix}), use (frac{1}{ad-bc}begin{bmatrix}d & -b \ -c & aend{bmatrix})
For larger matrices, form the augmented matrix ([A mid I])
Use row operations to transform the left side into the identity matrix
The right side becomes the inverse matrix
Alternatively, find the adjugate matrix and divide by the determinant
Verify by multiplying the matrix by its inverse to get the identity matrix