Question

$\text{A =}\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]\text{is an involutary matrix.}$

• A. True
• B. False

Answer 1

The correct option is A

True

$\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]A\times A=A^2=\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]=\left[\begin{array}{cc}0\times 0+1\times 1& 0\times 1+1\times 0\\ 1\times 0+0\times 1& 1\times 1+0\times 0\end{array}\right]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]=I$

(This is an identity matrix of order 2 $\times$ 2)

And A is a square matrix of order 2 $\times$ 2.

So all the conditions for involutary matrix are satisfied.

So A is an involutery matrix.