For a matrix (A=begin{pmatrix}a & b\ c & dend{pmatrix}), compute the determinant: (det(A)=ad-bc)
Check that (det(A)neq 0)
Swap the diagonal entries: (begin{pmatrix}d & b\ c & aend{pmatrix})
Change the signs of the off-diagonal entries: (begin{pmatrix}d & -b\ -c & aend{pmatrix})
Divide every entry by the determinant:
(A^{-1}=dfrac{1}{ad-bc}begin{pmatrix}d & -b\ -c & aend{pmatrix})