Question

matrix $A=\left[\begin{array}{ccc}-5& -8& 0\\ 3& 5& 0\\ 1& 2& -1\end{array}\right]$ is

• A. involutory.
• B. Skew-symmetric
• C. null
• D. diagonal

Answer 1

The correct option is A involutory.

$A^2=A.A=\left[\begin{array}{ccc}-5& -8& 0\\ 3& 5& 0\\ 1& 2& -1\end{array}\right]\times \left[\begin{array}{ccc}-5& -8& 0\\ 3& 5& 0\\ 1& 2& -1\end{array}\right]$
$=\left[\begin{array}{ccc}25-24+0& 40-40+0& 0+0+0\\ -15+15+0& -24+25+0& 0+0+0\\ -5+6-1& -8+10-2& 0+0+1\end{array}\right]$
$=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]=I$
Hence the given matrix is Involutory.