If A is defined by A=

$$\begin{bmatrix}

1 & 1 & 0 & -1 \\

2 & 1 & 0 & 1 \\

1 & 1 & 0 & 2 \\

1 & -1 & 1 & 1

\end{bmatrix}$$

find det (A) and det (P'AP), where P is defined in Prob. 18, and show that the two are equal. This result demonstrates Theorem 1.8.7.