Let A be 3×3 matrix such that A(123023011)=(001100010)then A−1=

A(123023011)=(001100010) ⇒c1−c3 A(321320110)=(100001010)c2−c3 A(312302101)=(100010001)⇒A−1= (312302101)

Let A be 3×3 matrix such that A(123023011)=(001100010)then A−1=

A(123023011)=(001100010) ⇒c1−c3 A(321320110)=(100001010)c2−c3 A(312302101)=(100010001)⇒A−1= (312302101)

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Let A be $3 \times 3$ matrix such that $A (\begin{matrix} 1 & 2 & 3 \\ 0 & 2 & 3 \\ 0 & 1 & 1 \end{matrix}) = (\begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix}) t h e n A^{- 1} =$

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$(\begin{matrix} 3 & 1 & 2 \\ 3 & 0 & 2 \\ 1 & 0 & 1 \end{matrix})$

$(\begin{matrix} 3 & 2 & 1 \\ 3 & 2 & 0 \\ 1 & 1 & 0 \end{matrix})$

$(\begin{matrix} 0 & 1 & 3 \\ 0 & 2 & 3 \\ 1 & 1 & 1 \end{matrix})$

$(\begin{matrix} 1 & 2 & 3 \\ 0 & 1 & 1 \\ 0 & 2 & 3 \end{matrix})$

answer is A.

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Detailed Solution

$A (\begin{matrix} 1 & 2 & 3 \\ 0 & 2 & 3 \\ 0 & 1 & 1 \end{matrix}) = (\begin{matrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{matrix}) \Rightarrow c_{1} - c_{3} A (\begin{matrix} 3 & 2 & 1 \\ 3 & 2 & 0 \\ 1 & 1 & 0 \end{matrix}) = (\begin{matrix} 1 & 0 & 0 \\ 0 & 0 & 1 \\ 0 & 1 & 0 \end{matrix})$

$c_{2} - c_{3} A (\begin{matrix} 3 & 1 & 2 \\ 3 & 0 & 2 \\ 1 & 0 & 1 \end{matrix}) = (\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}) \Rightarrow A^{- 1} = (\begin{matrix} 3 & 1 & 2 \\ 3 & 0 & 2 \\ 1 & 0 & 1 \end{matrix})$