Question

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

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

Answer 1

Answer: (C)

Null matrix

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