If A-1=1314-2-2-541-21 and |A| = 3 then Adj A=

A-1=13 14-2-2-541-21adjA3=13 14-2-2-541-21adjA=14-2-2-541-21

If A-1=1314-2-2-541-21 and |A| = 3 then Adj A=

A-1=13 14-2-2-541-21adjA3=13 14-2-2-541-21adjA=14-2-2-541-21

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If $A^{- 1} = \frac{1}{3} [\begin{matrix} 1 & 4 & - 2 \\ - 2 & - 5 & 4 \\ 1 & - 2 & 1 \end{matrix}]$ and |A| = 3 then Adj A=

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$3 [\begin{matrix} 1 & 4 & - 2 \\ - 2 & - 5 & 4 \\ 1 & - 2 & 1 \end{matrix}]$

$\frac{1}{3} [\begin{matrix} - 1 & - 4 & 2 \\ 2 & 5 & - 4 \\ - 1 & 2 & - 1 \end{matrix}]$

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

answer is C.

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Detailed Solution

$\begin{array}{rcl} A^{- 1} & = & \frac{1}{3} [\begin{matrix} 1 & 4 & - 2 \\ - 2 & - 5 & 4 \\ 1 & - 2 & 1 \end{matrix}] \\ \frac{ad j A}{3} & = & \frac{1}{3} [\begin{matrix} 1 & 4 & - 2 \\ - 2 & - 5 & 4 \\ 1 & - 2 & 1 \end{matrix}] \\ ad j A & = & [\begin{matrix} 1 & 4 & - 2 \\ - 2 & - 5 & 4 \\ 1 & - 2 & 1 \end{matrix}] \end{array}$