Given an example of two non-zero 2×2 matrices A and B such that A… - Vidyadip

Question

Given an example of two non-zero 2×2 matrices A and B such that AB = 0.

✓

Answer

Let,
$\text{A}=\begin{bmatrix}1&0\\0&0\end{bmatrix}\neq0$
$\text{B}=\begin{bmatrix}0&0\\0&1\end{bmatrix}\neq0$
$\text{AB}=\begin{bmatrix}1&0\\0&0\end{bmatrix}\begin{bmatrix}0&0\\0&1\end{bmatrix}$
$=\begin{bmatrix}0&0\\0&0\end{bmatrix}$
$=0$
So,
$\text{A}=\begin{bmatrix}1&0\\0&0\end{bmatrix}$
$\text{B}=\begin{bmatrix}0&0\\0&1\end{bmatrix}$

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