question_answer

If the matrices  B = adj A and \[C=3A,\]then \[\frac{|adj\,B|}{|C|}\]   is equal to [JEE MAIN Held on 09-01-2020 Morning]

A) 16

B) 2

C) 72                    

D) 8

Correct Answer: D

Solution :

[d] \[\frac{\left| adj\,\,B \right|}{\left| C \right|}=\frac{|adj\,\,(adj\,\,A)|}{\left| 3A \right|}=\frac{{{\left| A \right|}^{{{2}^{2}}}}}{{{3}^{3}}\left| A \right|}={{\left( \frac{\left| A \right|}{3} \right)}^{3}}\] Hence, \[\frac{|adj\,\,B|}{\left| C \right|}={{\left( \frac{6}{3} \right)}^{3}}=8\]