If A=22-32, B=0-110 then B-1 A-1-1=

A=22-32 B=0-110B-1 A-1=A-1-1 B-1-1 =AB =22-32 0-110 =2-223

If A=22-32, B=0-110 then B-1 A-1-1=

A=22-32 B=0-110B-1 A-1=A-1-1 B-1-1 =AB =22-32 0-110 =2-223

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If $A = (\begin{matrix} 2 & 2 \\ - 3 & 2 \end{matrix}), B = (\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix})$ then ${(B^{- 1} A^{- 1})}^{- 1} =$

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$(\begin{matrix} 2 & - 2 \\ 2 & 3 \end{matrix})$

$(\begin{matrix} 3 & - 2 \\ 2 & 2 \end{matrix})$

$\frac{1}{10} (\begin{matrix} 2 & 2 \\ - 2 & 3 \end{matrix})$

$\frac{1}{10} (\begin{matrix} 3 & 2 \\ - 2 & 2 \end{matrix})$

answer is A.

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Detailed Solution

$\begin{array}{rcl} A & = & (\begin{matrix} 2 & 2 \\ - 3 & 2 \end{matrix}) B = (\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}) \\ (B^{- 1} A^{- 1}) & = & {(A^{- 1})}^{- 1} {(B^{- 1})}^{- 1} \\ = & AB \\ = & [\begin{matrix} 2 & 2 \\ - 3 & 2 \end{matrix}] [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}] \\ = & [\begin{matrix} 2 & - 2 \\ 2 & 3 \end{matrix}] \end{array}$