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If $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$ then show that $|2 A|=4|A|$.
If $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$ then show that $|2 A|=4|A|$.
CBSE | Class 12 | Determinants | Exercise 4.1 | Maths | NCERT
If $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$ then show that $|2 A|=4|A|$.

$A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$

$2 \mathrm{~A}=\left[\begin{array}{ll}2 & 4 \\ 8 & 4\end{array}\right]$

L.H.S. $=|2 A|=\left|\begin{array}{ll}2 & 4 \\ 8 & 4\end{array}\right|=8-32=-24$

R.H.S. $=4|\mathrm{~A}|=4\left|\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right|=4(2-8)=-24$

LHS $=$ RHS

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