If A = 2 3 - 3 2 , B = 0 - 1 1 0 then ( B − 1 A − 1 ) − 1 =

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Question: Answered & Verified by Expert

If

A = [\begin{matrix} 2 & 3 \\ - 3 & 2 \end{matrix}], B = [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]

then

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

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Options:

A $[\begin{matrix} 3 & - 2 \\ 2 & 3 \end{matrix}]$
B $[\begin{matrix} 2 & 2 \\ - 2 & 3 \end{matrix}]$
C $[\begin{matrix} 2 & - 3 \\ 2 & 2 \end{matrix}]$
D $[\begin{matrix} 1 & - 1 \\ - 2 & 3 \end{matrix}]$

Solution:

2249 Upvotes Verified Answer

The correct answer is:

[\begin{matrix} 3 & - 2 \\ 2 & 3 \end{matrix}]

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

= A B

= [\begin{matrix} 2 & 3 \\ - 3 & 2 \end{matrix}] [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]

= [\begin{matrix} 3 & - 2 \\ 2 & 3 \end{matrix}]

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