Question

If $A=\left[\begin{array}{cc}1& 0\\ 2& 0\end{array}\right]$ and $B=\left[\begin{array}{cc}0& 0\\ 1& 12\end{array}\right]$ , then

• A. AB = O, BA = O
• B. AB = O, BA $\ne$ O
• C. AB $\ne$ O, BA = O
• D. AB $\ne$ O, BA $\ne$ O

Answer 1

Answer: (B)

Here, $AB=\left[\begin{array}{cc}1& 0\\ 2& 0\end{array}\right]\left[\begin{array}{cc}0& 0\\ 1& 12\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]$
and $BA=\left[\begin{array}{cc}0& 0\\ 1& 12\end{array}\right]\left[\begin{array}{cc}1& 0\\ 2& 0\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 25& 0\end{array}\right]\ne O.$