If A = [ * 20 c 1&2 4&2 ], then show that |2A| = 4|A| - Vidyadip

Question

If $A = \left[ {\begin{array}{*{20}{c}} 1&2 \\ 4&2 \end{array}} \right]$, then show that |2A| = 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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