How do you invert a 2x2 matrix?

Take a matrix A=(^a_c^b_d), where a,b,c,d are numbers.

First find the determinant. This is ad-bc.

Now, rearrange the matrix to become (^d_-c^-b_a). Divide this by the determinant, to have A^-1=¹/_(ad-bc)(^d_-c^-b_a). This is the inverse of A.