Let A & = [ ccc 3 & 2 & -1 -2 & 5 & 4 ]_ 2 3 , B & = [ cc 3 & -3 … - Vidyadip

Question

$
\begin{aligned}
\text { Let } A & =\left[\begin{array}{ccc}
3 & 2 & -1 \\
-2 & 5 & 4
\end{array}\right]_{2 \times 3}, \\
B & =\left[\begin{array}{cc}
3 & -3 \\
-4 & 2
\end{array}\right]_{2 \times 2}
\end{aligned}
$
Find $\mathrm{AB}$ and $\mathrm{BA}$ which ever exist.

✓

Answer

Since number of columns of $A \neq$ number of rows of $B$. Product of $A B$ is not defined. But number of columns of $B=$ number of rows of $A=2$, the product BA exists,
$
\begin{aligned}
\therefore \mathrm{BA} & =\left[\begin{array}{cc}
3 & -3 \\
-4 & 2
\end{array}\right]\left[\begin{array}{ccc}
3 & 2 & -1 \\
-2 & 5 & 4
\end{array}\right] \\
& =\left[\begin{array}{ccc}
9+6 & 6-15 & -3-12 \\
-12-4 & -8+10 & 4+8
\end{array}\right] \\
& =\left[\begin{array}{ccc}
15 & -9 & -15 \\
-16 & 2 & 12
\end{array}\right]
\end{aligned}
$

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