Question

If the matrix AB is zero, then
(a) It is not necessary that either A = O or, B = O
(b) A = O or B = O
(c) A = O and B = O
(d) all the above statements are wrong

Answer 1

(a) It is not necessary that either A = O or, B = O


$$\begin{gathered} \mathrm{Let}A=\left[\begin{array}{cc}0& 2\\ 0& 0\end{array}\right]\mathrm{and}B=\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right] \\ \therefore AB=\left[\begin{array}{cc}0& 2\\ 0& 0\end{array}\right]\left[\begin{array}{cc}1& 0\\ 0& 0\end{array}\right]=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right] \end{gathered}$$