A= [ cc -1 & -2 -3 & 2 1 & 0 ]_ 3 2 , B= [ cc 1 & 2 -1 & -2 ]_ 2 2 Find AB and BA which ever exist.

Here A is order of 3 2 and B is of order 2 2. By conformability of product, A B is defined but BA is not defined. AB & = [ cc -1 & -2 -3 & 2 1 & 0 ] [ cc 1 & 2 -1 & -2 ] & = [ cc -1+2 & -2+4 -3-2 & -6-4 1+0 & 2+0 ]= [ cc 1 & 2 -3 & -10 1 & 0 ]

A= [ cc -1 & -2 -3 & 2 1 & 0 ]_ 3 2 , B= [ cc 1 & 2 -1 & -2 ]_ 2 …

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Question

$A=\left[\begin{array}{cc}
-1 & -2 \\
-3 & 2 \\
1 & 0
\end{array}\right]_{3 \times 2}, B=\left[\begin{array}{cc}
1 & 2 \\
-1 & -2
\end{array}\right]_{2 \times 2}
$
Find $\mathrm{AB}$ and $\mathrm{BA}$ which ever exist.

✓

Answer

Here A is order of $3 \times 2$ and B is of order $2 \times 2$. By conformability of product, $A B$ is defined but $\mathrm{BA}$ is not defined.
$
\begin{aligned}
\therefore \mathrm{AB} & =\left[\begin{array}{cc}
-1 & -2 \\
-3 & 2 \\
1 & 0
\end{array}\right]\left[\begin{array}{cc}
1 & 2 \\
-1 & -2
\end{array}\right] \\
& =\left[\begin{array}{cc}
-1+2 & -2+4 \\
-3-2 & -6-4 \\
1+0 & 2+0
\end{array}\right]=\left[\begin{array}{cc}
1 & 2 \\
-3 & -10 \\
1 & 0
\end{array}\right]
\end{aligned}
$

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