25. Let the 2k x 2k matrix A be partitioned as follows

$$

A =

\begin{bmatrix}

A_{11} & A_{12} \\

A_{21} & A_{22}

\end{bmatrix}

$$

where $A_{11}$ is a k x k matrix; further suppose that $A_{21}A_{22}=A_{22}A_{21}$, and let

$|A_{22}| eq 0$. Show that det(A) = det($A_{11}A_{22}-A_{12}A_{21}$).

(Use Theorem 8.2.1.)