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If A={bmatrix} 2 & 0 & 0 0 & 2 & 0 0 & 0 & 2 {bmatrix}, then

Question

If $A = ⎣ ⎡ 200020002 ⎦ ⎤$ , then value of $A^{- 1}$ is

⎣ ⎡ 100010111 ⎦ ⎤

⎣ ⎡ \frac{1}{2} 00 0 \frac{1}{2} 0 00 \frac{1}{2} ⎦ ⎤

⎣ ⎡ 200 0 - 2 0 00 - 2 ⎦ ⎤

None of these

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Isabella Discussed

A = ⎣ ⎡ 200020002 ⎦ ⎤

, then value of

A^{- 1}

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Text solutionVerified

A = ⎣ ⎡ 200020002 ⎦ ⎤ = 2 ⎣ ⎡ 100010001 ⎦ ⎤ = 2 I

\Rightarrow A A^{- 1} = 2 I A^{- 1}

\Rightarrow I = 2 A^{- 1}

\Rightarrow A^{- 1} = ⎣ ⎡ \frac{1}{2} 00 0 \frac{1}{2} 0 00 \frac{1}{2} ⎦ ⎤

Ans: B

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