Question

If A = $\left[\begin{array}{cc}i& 0\\ 0& -i\end{array}\right]$ B= $\left[\begin{array}{cc}0& -1\\ 1& 0\end{array}\right]$ and C = $\left[\begin{array}{cc}0& i\\ i& 0\end{array}\right]$ then AB $\ne$

• A. - BA
• B. - C
• C. BA
• D. AB

Answer 1

The correct option is C BA

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