If \( M = \begin{bmatrix} 2 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 2 \end{bmatrix} \), then what is the value of \( |M| |adjM| \) ?

Explanation

The determinant |M| is 2 \times 2 \times 2 = 8. Using the property |adjM| = |M|^(n-1), for a 3x3 matrix |adjM| = 8^2 = 64. Their product |M||adjM| is 8 \times 64 = 512.

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