Check that the matrix is square
Compute the determinant
If the determinant is zero, the matrix is not invertible
Form the augmented matrix [A | I]
Use row operations to transform the left side into the identity matrix
The right side becomes the inverse matrix
For a 2×2 matrix [[a, b], [c, d]], use 1/(ad – bc) times [[d, -b], [-c, a]]
Verify the result by multiplying the matrix by its inverse to get the identity matrix