Question:
Show by an example that for A ≠ 0, B ≠ 0, AB = 0.
Solution:
Let $A=\left[\begin{array}{ll}0 & 1 \\ 0 & 2\end{array}\right] \neq O$ and $B=\left[\begin{array}{cc}-1 & 1 \\ 0 & 0\end{array}\right] \neq O$
So, the product $A B=\left[\begin{array}{ll}0 & 1 \\ 0 & 2\end{array}\right]\left[\begin{array}{cc}-1 & 1 \\ 0 & 0\end{array}\right]=\left[\begin{array}{ll}0 & 0 \\ 0 & 0\end{array}\right]=O$
– Hence Proved
$A=\left[\begin{array}{lll}2 & 4 & 0 \\ 3 & 9 & 6\end{array}\right]$ and $B=\left[\begin{array}{ll}1 & 4 \\ 2 & 8 \\ 1 & 3\end{array}\right]$
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