$If A = [\begin{array}{ccc} 2 & 2 & 1 \\ - 1 & 0 & 2 \\ 4 & 1 & 0 \end{array}] then 11 A^{- 1} =$

Moderate

A

$[\begin{matrix} 2 & 1 & 4 \\ 8 & - 4 & - 5 \\ - 1 & - 6 & - 2 \end{matrix}]$
B

$[\begin{matrix} 2 & 1 & 4 \\ 8 & 4 & 5 \\ 1 & 6 & 2 \end{matrix}]$
C

$[\begin{matrix} - 2 & - 1 & - 4 \\ 8 & - 4 & - 5 \\ - 1 & 6 & 2 \end{matrix}]$
D

$[\begin{matrix} - 2 & 1 & 4 \\ 8 & - 4 & - 5 \\ - 1 & 6 & 2 \end{matrix}]$

Solution

$\begin{array}{l} \det A = 2 (0 - 2) - 2 (0 - 8) + (- 1 - 0) \\ = - 4 + 16 - 1 \\ = 11 \end{array}$
$11 A^{- 1} = A d j A = [\begin{matrix} A_{11} & A_{21} & A_{31} \\ A_{12} & A_{22} & A_{32} \\ A_{13} & A_{23} & A_{33} \end{matrix}] = [\begin{matrix} - 2 & 1 & 4 \\ 8 & - 4 & - 5 \\ - 1 & 6 & 2 \end{matrix}]$

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