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

Question

Dr. Abubacker · Accepted Answer

(a)
$A$ is involuntary. Hence,
$A^{2} = I \Rightarrow A = A^{- 1}$
Also,
$(kA)^{- 1} = \frac{1}{k}(A)^{- 1}$
$\Rightarrow \left( \frac{1}{2}A \right)^{- 1} = 2(A)^{- 1} \Rightarrow 2A$

Q. $A$ is an involuntary matrix given by $A = \begin{bmatrix} 0 & 1 & - 1 \\ 4 & - 3 & 4 \\ 3 & - 3 & 4 \end{bmatrix}$ , then the inverse of $\frac{A}{2}$ will be

Explanation

Reviewed by Dr. Abubacker

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