A is an involuntary matrix given by A=01−14−343−34, then the inverse of A/2 will be

A is involuntary. HenceA2=I⇒A=A−1Also,(kA)−1=1k(A)−1 Or 12A−1=2(A)−1 or 2A

A is an involuntary matrix given by A=01−14−343−34, then the inverse of A/2 will be

A is involuntary. HenceA2=I⇒A=A−1Also,(kA)−1=1k(A)−1 Or 12A−1=2(A)−1 or 2A

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$A is an involuntary matrix given by A = [\begin{array}{ccc} 0 & 1 & - 1 \\ 4 & - 3 & 4 \\ 3 & - 3 & 4 \end{array}], then the inverse of A / 2 will be$

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$\frac{A^{- 1}}{2}$

$\frac{A}{2}$

$A^{2}$

answer is A.

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Detailed Solution

A is involuntary. Hence
$A^{2} = I \Rightarrow A = A^{- 1}$
Also,
$\begin{array}{l} (kA)^{- 1} = \frac{1}{k} (A)^{- 1} \\ Or {(\frac{1}{2} A)}^{- 1} = 2 (A)^{- 1} or 2 A \end{array}$

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