If A= [ rr 5 & -1 6 & 7 ] and B= [ ll 2 & 1 3 & 4 ], then which o… - Vidyadip

MCQ

If $A=\left[\begin{array}{rr}5 & -1 \\ 6 & 7\end{array}\right]$ and $B=\left[\begin{array}{ll}2 & 1 \\ 3 & 4\end{array}\right]$, then which of the following is correct ?

A
$AB =\left[\begin{array}{cc}7 & -1 \\ 9 & 22\end{array}\right]$
B
$BA =\left[\begin{array}{rr}16 & -5 \\ 39 & 25\end{array}\right]$
C
$AB = BA$
✓
$A B \neq B A$

✓

Answer

Correct option: D.

$A B \neq B A$

(d) $A B \neq B A$
Explanation:
We have,
$AB =\left[\begin{array}{rr}5 & -1 \\ 6 & 7\end{array}\right]\left[\begin{array}{ll}2 & 1 \\ 3 & 4\end{array}\right]$
$\begin{array}{l}=\left[\begin{array}{cc}10-3 & 5-4 \\ 12-21 & 6-28\end{array}\right] \\ =\left[\begin{array}{rr}7 & 1 \\ -9 & -22\end{array}\right]\end{array}$
$\begin{array}{l} BA =\left[\begin{array}{ll}2 & 1 \\ 3 & 4\end{array}\right]\left[\begin{array}{rr}5 & -1 \\ 6 & 7\end{array}\right] \\ =\left[\begin{array}{rr}10+6 & -2+7 \\ 15+24 & -3+28\end{array}\right]=\left[\begin{array}{cc}16 & 5 \\ 39 & 25\end{array}\right]\end{array}$
So, $AB = BA$.

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