Question

If $A=\left[\begin{array}{cc}0& -i\\ i& 0\end{array}\right]$, $B=\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$, then $AB+BA$ is

• A. null matrix
• B. unit matrix
• C. invertible matrix
• D. none of these

Answer 1

The correct option is A null matrix

$A=\left[\begin{array}{cc}0& -i\\ i& 0\end{array}\right],B=\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$
$AB+BA=\left[\begin{array}{cc}0& -i\\ i& 0\end{array}\right]\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]+\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]\left[\begin{array}{cc}0& -i\\ i& 0\end{array}\right]=\left[\begin{array}{cc}0& i\\ i& 0\end{array}\right]+\left[\begin{array}{cc}0& -i\\ -i& 0\end{array}\right]=0$