Let the matrix be (A)
Check that (det(A) neq 0)
Compute the determinant of (A)
Find the matrix of minors
Convert the matrix of minors into the matrix of cofactors by applying signs
Transpose the cofactor matrix to get the adjugate matrix (operatorname{adj}(A))
Use the formula (A^{-1} = frac{1}{det(A)} operatorname{adj}(A))
Multiply every entry of the adjugate matrix by (frac{1}{det(A)})
Write the resulting matrix as (A^{-1})