Check that the matrix is square
Compute the determinant
If the determinant is 0, the matrix has no inverse
If the determinant is nonzero, proceed
For a 2×2 matrix, use the formula
For larger matrices, use row reduction or the adjugate method
Set up the matrix next to the identity matrix
Perform row operations until the left side becomes the identity matrix
The right side becomes the inverse
Verify by multiplying the matrix by its inverse
Confirm the product is the identity matrix