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

$$

A=

\begin{bmatrix}

A_{11} & A_{12}\\

A_{21} & A_{22}

\end{bmatrix}

$$

where *A₁₁* is a *k* x *k* matrix; further suppose that *A₂₁A₂₂* = *A₂₂A₂₁* and let

|*A₂₂*| ≠ 0. Show that det (A) = det (A₁₁A₂₂ - A₁₂A₂₁).

(Use Theorem 8.2.1.)