Question

If $A=\left[\begin{array}{ccc}4& -1& -4\\ 3& 0& -4\\ 3& -1& -3\end{array}\right]$ then $A^2$ is equal to

• A. $A$
• B. $I$
• C. $A^T$
• D. none of these

Answer 1

Answer: (B)

$I$

Given, $A=\left[\begin{array}{ccc}4& -1& -4\\ 3& 0& -4\\ 3& -1& -3\end{array}\right]$
$A^2=\left[\begin{array}{ccc}4& -1& -4\\ 3& 0& -4\\ 3& -1& -3\end{array}\right]\left[\begin{array}{ccc}4& -1& -4\\ 3& 0& -4\\ 3& -1& -3\end{array}\right]=\left[\begin{array}{ccc}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$
$\Rightarrow A^2=I$