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For any 4 x 4...

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For any 4 x 4 matrix A, if adjA. adj(adjA)0 8 0 0then \vert Al isIS0 0 0 8(2) 8(3) 2(4) 8

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Q. If A is a square matrix such that A (AdjA) =

⎛ ⎜ ⎝ \begin{matrix} 4 & 0 & 0 0 & 4 & 0 0 & 0 & 4 \end{matrix} ⎞ ⎟ ⎠

then det (AdjA) =

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 4 6 & 2 & 8 2 & 4 & 6 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 8 & 4 & - 2 0 & - 2 & 0 2 & 2 & 6 \end{matrix} ⎤ ⎥ ⎦

C = ⎡ ⎢ ⎣ \begin{matrix} 8 & 2 & 0 0 & - 2 & - 6 - 8 & 4 & - 10 \end{matrix} ⎤ ⎥ ⎦

A - B - C

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 4 6 & 2 & 8 2 & 4 & 6 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 8 & 4 & - 2 0 & - 2 & 0 2 & 2 & 6 \end{matrix} ⎤ ⎥ ⎦

C = ⎡ ⎢ ⎣ \begin{matrix} 8 & 2 & 0 0 & - 2 & - 6 - 8 & 4 & - 10 \end{matrix} ⎤ ⎥ ⎦

A + B + C

Given that the determinant of the matrix ⎡ ⎢ ⎣ \begin{matrix} 2 & 6 & 0 4 & 12 & 8 - 2 & 0 & 4 \end{matrix} ⎤ ⎥ ⎦ is - 96, the determinant of the matrix ⎡ ⎢ ⎣ \begin{matrix} 4 & 12 & 0 8 & 24 & 16 - 4 & 0 & 8 \end{matrix} ⎤ ⎥ ⎦ is

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & 0 & 4 6 & 2 & 8 2 & 4 & 6 \end{matrix} ⎤ ⎥ ⎦, B = ⎡ ⎢ ⎣ \begin{matrix} 8 & 4 & - 2 0 & - 2 & 0 2 & 2 & 6 \end{matrix} ⎤ ⎥ ⎦

C = ⎡ ⎢ ⎣ \begin{matrix} 8 & 2 & 0 0 & - 2 & - 6 - 8 & 4 & - 10 \end{matrix} ⎤ ⎥ ⎦

(3 A + 2 B) - 3 C

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