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Matrices (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Matrices (p-1)3 Marks
Question
If $A=\left[\begin{array}{ll}3 & 1 \\ 1 & 5\end{array}\right], B=\left[\begin{array}{cc}1 & 2 \\ 5 & -2\end{array}\right]$, verify $|A B|=|A||B|$.
✓

Answer

$
\begin{aligned}
& AB =\left[\begin{array}{ll}
3 & 1 \\
1 & 5
\end{array}\right]\left[\begin{array}{rr}
1 & 2 \\
5 & -2
\end{array}\right] \\
&=\left[\begin{array}{rr}
3+5 & 6-2 \\
1+25 & 2-10
\end{array}\right]=\left[\begin{array}{rr}
8 & 4 \\
26 & -8
\end{array}\right] \\
& \therefore| AB |=\left|\begin{array}{rr}
8 & 4 \\
26 & -8
\end{array}\right| \\
&=-64-104=-168.....(1) \\
&| A |=\left|\begin{array}{rr}
3 & 1 \\
1 & 5
\end{array}\right|=15-1=14 \\
&| B |=\left|\begin{array}{rr}
1 & 2 \\
5 & -2
\end{array}\right|=-2-10=-12 \\
& \therefore| A || B |=14(-12)=-168....(2)
\end{aligned}
$
From (1) and (2), $| AB |=| A || B |$.

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