If $A=\begin{bmatrix}1&0\\0&0\end{bmatrix},B=\begin{bmatrix}0&0\\3&0\end{bmatrix}$ then
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $AB≠0, BA≠0$
Given matrices:
$A = \begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix}$, $B = \begin{bmatrix}0 & 0 \\ 3 & 0\end{bmatrix}$
Compute $AB$:
$AB = \begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix} \begin{bmatrix}0 & 0 \\ 3 & 0\end{bmatrix} = \begin{bmatrix}0 & 0 \\ 0 & 0\end{bmatrix} = 0$
Compute $BA$:
$BA = \begin{bmatrix}0 & 0 \\ 3 & 0\end{bmatrix} \begin{bmatrix}1 & 0 \\ 0 & 0\end{bmatrix} = \begin{bmatrix}0 & 0 \\ 3 & 0\end{bmatrix} = B \neq 0$
Correct statements: $AB = 0, BA \neq 0$