If A= 1&2 3&-1 and B= 1&0 -1&0 , find |AB|. - Vidyadip

Question

If $\text{A}=\begin{bmatrix}1&2\\3&-1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\-1&0\end{bmatrix},$ find |AB|.

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Answer

$\text{A}=\begin{bmatrix}1&2\\3&-1\end{bmatrix}$
$\text{B}=\begin{bmatrix}1&0\\-1&0\end{bmatrix}$
$\text{AB}=\begin{bmatrix}1&2\\3&-1\end{bmatrix}\begin{bmatrix}1&0\\-1&0\end{bmatrix}$
$=\begin{bmatrix}1-2&0+0\\3+1&0+0\end{bmatrix}=\begin{bmatrix}-1&0\\4&0\end{bmatrix}$
$|\text{AB}|=0-0=0$

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