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Question: If A is an involuntary matrix given by A = \(\begin{bmatrix} 0 & 1 & - 1 \\ 4 & - 3 & 4 \\ 3 & - 3 &...

If A is an involuntary matrix given by A = [01−14−343−34]\begin{bmatrix} 0 & 1 & - 1 \\ 4 & - 3 & 4 \\ 3 & - 3 & 4 \end{bmatrix}then the inverse of A2\frac{A}{2}will be

A

2A

B

A−12\frac{A^{- 1}}{2}

C

A2\frac{A}{2}

D

A2

Answer

2A

Explanation

Solution

Q A2 = I (given A is involutory)

So A. A = I Ž A2\frac{A}{2}. 2A = I