Question

If $A=\left[\begin{array}{ccc}1& 0& 1\\ 0& 0& 0\\ 1& 0& 1\end{array}\right]$ then $A^2$ is equal to

• A. $A$
• B. $-A$
• C. $2A$
• D. $-2A$

Answer 1

The correct option is C $2A$

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

$A^2=\left[\begin{array}{ccc}2& 0& 2\\ 0& 0& 0\\ 2& 0& 2\end{array}\right]$

$A^2=2\left[\begin{array}{ccc}1& 0& 1\\ 0& 0& 0\\ 1& 0& 1\end{array}\right]=2A$

$\therefore A^2=2A$.