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If \(A = \left[ {\begin{array}{*{20}{c}} 1&2 \\ 4&2 \end{array}} \right]\), then show that |2A| = 4|A|
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MathsClass 12

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

Answer

\(2A = 2\left[ {\begin{array}{*{20}{c}} 1&2 \\ 4&2 \end{array}} \right]\)
\(= \left[ {\begin{array}{*{20}{c}} 2&4 \\ 8&4 \end{array}} \right] \)
therefore, |2A| = 8 - 32 = -24
Now, |A| = 2 - 8 = -6
therefore, 4|A| = -24
Hence Proved.
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