If A= [ ll 1 & 2 4 & 2 ], then show that |2 A |=4| A | - Vidyadip

Question

If $A=\left[\begin{array}{ll}1 & 2 \\ 4 & 2\end{array}\right]$, then show that $|2 A |=4| A |$

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Answer

$2A = 2\left[ {\begin{array}{*{20}{c}} 1&2 \\ 4&2 \end{array}} \right]$

$= \left[ {\begin{array}{*{20}{c}} 2&4 \\ 8&4 \end{array}} \right] $

|2A| = 8 - 32 = -24

|A| = 2 - 8 = -6

4|A| = -24

Hence Proved.

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