Question

If the matrix AB is zero, then

Options

• It is not necessary that either A = O or, B = O

• A = O or B = O

• A = O and B = O

• all the above statements are wrong

Answer 1

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

\[ \text{Let A}= \begin{bmatrix}0 & 2 \\ 0 & 0\end{bmatrix} \text{and B}= \begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix}\]

\[ \therefore AB = \begin{bmatrix}0 & 2 \\ 0 & 0\end{bmatrix}\begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix} = \begin{bmatrix}0 & 0 \\ 0 & 0\end{bmatrix}\]