Question

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

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

Answer 1

The correct option is B $\frac{A^{-1}}{2}$

Given $A$ to be involutory matrix, then according to the definition of involutory matrix we have, $A^2=I$. [ $I$ being identity matrix of order $3$].

So,

$A^2=I$

or, $A=A^{-1}$ [ Since involutory matrix is always invertible]

or, $\frac{A}{2}=\frac{A^{-1}}{2}$.