Same Variable Matrices in Matrix Thereom

The Same Variable Matrices in Matrix Thereom states that:

$\begin{bmatrix} \begin{bmatrix} a & c\\ b & d \end{bmatrix} & \begin{bmatrix} c & a\\ b & d \end{bmatrix}\\ \begin{bmatrix} a & c\\ d & b \end{bmatrix} & \begin{bmatrix} c & a\\ d & b \end{bmatrix} \end{bmatrix} = 4abcd - {ab}^2 - {bc}^2 - {cd}^2 - {ad}^2$