If A = , then show that |2A| = 4|A|

A = 2A = L.H.S. = |2A| = | * 20 r 2&4 8&4 | = 8 - 32 = - 24 R.H.S. = 4|A| = 4 | * 20 r 1&2 4&2 | = 4(2 - 8) = - 24 Hence, |2A| = 4|A|

Determinants — Class 12 Maths Solution

ncert exercise SA NCERT,Ex.4.1,Q.3,Page.108

Question

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

Step-by-step Solution

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

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

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, $|2A| = 4|A|$

NCERT & Exemplar solution for CBSE Class 12 Mathematics, Determinants. Curated by Sachin Sharma. Free for all students.