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If $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$, then show that $|2 A|=4|A|$.
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Verified Answer
$A=\left[\begin{array}{ll}
1 & 2 \\
4 & 2
\end{array}\right] \Rightarrow 2 \mathrm{~A}=\left[\begin{array}{ll}
2 & 4 \\
8 & 4
\end{array}\right]$
L.H.S $=|2 \mathrm{~A}|=\left[\begin{array}{ll}2 & 4 \\ 8 & 4\end{array}\right]=-24$
R.H.S $=4|\mathrm{~A}|=4\left|\begin{array}{ll}1 & 2 \\ 4 & 4\end{array}\right|=-24$
Hence $|2 \mathrm{~A}|=4|\mathrm{~A}|$.
1 & 2 \\
4 & 2
\end{array}\right] \Rightarrow 2 \mathrm{~A}=\left[\begin{array}{ll}
2 & 4 \\
8 & 4
\end{array}\right]$
L.H.S $=|2 \mathrm{~A}|=\left[\begin{array}{ll}2 & 4 \\ 8 & 4\end{array}\right]=-24$
R.H.S $=4|\mathrm{~A}|=4\left|\begin{array}{ll}1 & 2 \\ 4 & 4\end{array}\right|=-24$
Hence $|2 \mathrm{~A}|=4|\mathrm{~A}|$.
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