Question

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

• A. $2A$
• B. $\frac{A^{-1}}{2}$
• C. $\frac{A}{2}$
• D. $A^2$

Answer 1

The correct option is A $2A$

Given A is an involutory matrix
$A^2=I$
$\Rightarrow AA=I$
So, for A , its inverse is A itself
Now, $\frac{A}{2}2A=I$
So, the inverse of $\frac{A}{2}$ is $2A$