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If $A = [\begin{matrix} 1 & 0 & 2 \\ 1 & - 1 & 0 \\ 2 & 1 & - 2 \end{matrix}]$ then $[A (A d J A) A^{- 1}] A =$

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$2 I$

$8 I$

$7 I$

$I$

answer is D.

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Detailed Solution

$[A (A d j A) A^{- 1}] A = [| A | . I . A^{- 1}] A$

$| A | = 1 (2 - 0) - 0 + 2 (1 + 2)$

$= | A | . I . I = | A | I$

$= 2 + 6 = 8$

$= 8 I$

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