If $A = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&2\\4&2\end{array}} \right]$, then show that $|2A| = 4|A|$
If $A = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&2\\4&2\end{array}} \right]$, then show that $|2A| = 4|A|$
Official Solution
VVidaara Team
✓ Verified solution
NCERT & Exemplar
$A = \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&2\\4&2\end{array}} \right]\therefore 2A$
$= \left[ {\begin{array}{rrrrrrrrrrrrrrrrrrrr}2&4\\8&4\end{array}} \right]$
L.H.S. $=$ $|2A| = \left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}2&4\\8&4\end{array}} \right| = 8 - 32 = - 24$
R.H.S. $=$ $4|A| = 4\left| {\begin{array}{rrrrrrrrrrrrrrrrrrrr}1&2\\4&2\end{array}} \right| = 4(2 - 8) = - 24$
Hence, $|2A| = 4|A|$
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