If the product of the matrix B=[264101−11−1] with a matrix A has inverse C=[−101113202] then A−1=

(BA)−1=C ⇒ A−1B−1=C ⇒ A−1=CB =[−3−5−50922146]

If the product of the matrix B=[264101−11−1] with a matrix A has inverse C=[−101113202] then A−1=

(BA)−1=C ⇒ A−1B−1=C ⇒ A−1=CB =[−3−5−50922146]

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If the product of the matrix $B = [\begin{matrix} 2 & 6 & 4 \\ 1 & 0 & 1 \\ - 1 & 1 & - 1 \end{matrix}]$ with a matrix A has inverse $C = [\begin{matrix} - 1 & 0 & 1 \\ 1 & 1 & 3 \\ 2 & 0 & 2 \end{matrix}]$ then $A^{- 1} =$

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$[\begin{matrix} - 3 & - 5 & 5 \\ 0 & 9 & 14 \\ 2 & 2 & 6 \end{matrix}]$

$[\begin{matrix} - 3 & - 5 & - 5 \\ 0 & 9 & 2 \\ 2 & 14 & 6 \end{matrix}]$

$[\begin{matrix} - 3 & 5 & 5 \\ 0 & 0 & 9 \\ - 1 & 1 & - 1 \end{matrix}]$

$[\begin{matrix} - 3 & - 3 & - 5 \\ 0 & 9 & 2 \\ 2 & 14 & 16 \end{matrix}]$

answer is C.

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Detailed Solution

${(B A)}^{- 1} = C$

$\Rightarrow A^{- 1} B^{- 1} = C$

$\Rightarrow A^{- 1} = C B$

$= [\begin{matrix} - 3 & - 5 & - 5 \\ 0 & 9 & 2 \\ 2 & 14 & 6 \end{matrix}]$

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If the product of the matrix B=[264101−11−1] with a matrix A has inverse C=[−101113202] then A−1=

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If the product of the matrix $B = [\begin{matrix} 2 & 6 & 4 \\ 1 & 0 & 1 \\ - 1 & 1 & - 1 \end{matrix}]$ with a matrix A has inverse $C = [\begin{matrix} - 1 & 0 & 1 \\ 1 & 1 & 3 \\ 2 & 0 & 2 \end{matrix}]$ then $A^{- 1} =$