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$If A = [\begin{array}{lll} 0 1 2 \\ 1 2 3 \\ 3 x 1 \end{array}] and A^{- 1} = [\begin{array}{ccc} 1 / 2 & - 1 / 2 & 1 / 2 \\ - 4 & 3 & y \\ 5 / 2 & - 3 / 2 & 1 / 2 \end{array}], then$

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x=1, y=-1

x=-1 , y=1

x=2 , y=-1/2

x=1/2 , y=1/2

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detailed solution

Correct option is A

We have 1 0 00 1 00 0 1=AA−1=0121233x11/2−1/21/2−43y5/2−3/21/2=10y+1012(y+1)41−x3x−12+xy⇒1−x=0,x−1=0,y+1=0,2+xy=1⇒x=1,y=−1.

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If A=0 1 21 2 33 x 1 and A−1=1/2−1/21/2−43y5/2−3/21/2, then

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$If A = [\begin{array}{lll} 0 1 2 \\ 1 2 3 \\ 3 x 1 \end{array}] and A^{- 1} = [\begin{array}{ccc} 1 / 2 & - 1 / 2 & 1 / 2 \\ - 4 & 3 & y \\ 5 / 2 & - 3 / 2 & 1 / 2 \end{array}], then$