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Determinants and Matrices — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsDeterminants and Matrices2 Marks
Question
Let $A=\left[\begin{array}{cc}4 & -3 \\ 5 & 2\end{array}\right]$ and $B=\left[\begin{array}{cc}-1 & 3 \\ 4 & -2\end{array}\right]$ Find $\mathrm{AB}$ and $\mathrm{BA}$ which ever exist.
✓

Answer

Since A and B are two matrix of same order $2 \times 2$.
$\therefore$ Both the product $\mathrm{AB}$ and $\mathrm{BA}$ exist and are of same order $2 \times 2$
$
\begin{aligned}
& \mathrm{AB}=\left[\begin{array}{cc}
4 & -3 \\
5 & 2
\end{array}\right]\left[\begin{array}{cc}
-1 & 3 \\
4 & -2
\end{array}\right] \\
&=\left[\begin{array}{cc}
-4-12 & 12+6 \\
-5+8 & 15-4
\end{array}\right]=\left[\begin{array}{cc}
-16 & 18 \\
3 & 11
\end{array}\right] \\
& \mathrm{BA}=\left[\begin{array}{cc}
-1 & 3 \\
4 & -2
\end{array}\right]\left[\begin{array}{cc}
4 & -3 \\
5 & 2
\end{array}\right]=\left[\begin{array}{cc}
-4+15 & 3+6 \\
16-10 & -12-4
\end{array}\right] \\
&=\left[\begin{array}{cc}
11 & 9 \\
6 & -16
\end{array}\right] \\
& \text { Here } \mathrm{AB} \neq \mathrm{BA}
\end{aligned}
$

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