Question: 3. If B = $$ begin{bmatrix} -I & A-I A-I & A end{bmatrix} $$, where A is an m x m symmetric matrix such

3. If B = $$

\begin{bmatrix}

-I & A-I \\

A-I & A

\end{bmatrix}

$$, where A is an m x m symmetric matrix such that A² = A, show that |B| = (-1)m.

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