KVPY Sample Paper KVPY Stream-SX Model Paper-13

If A, B and C are \[n\times n\] matrices and \[det(A)=2,\text{ }det(B)=3\] and \[det(C)=5,\] then the value of det \[({{A}^{2}}B{{C}^{-1}})\] is

A) \[\frac{6}{5}\]

B) \[\frac{12}{5}\]

C) \[\frac{18}{5}\]

D) \[\frac{24}{5}\]

Correct Answer: B

Solution :

We have, \[det(A)=2det(B)=3,det(C)=5\]

\[\Rightarrow \]\[\det \,({{A}^{2}}B{{C}^{-1}})=\det (A)\times \det (A)\times \det (B)\times \frac{1}{\operatorname{detC}}\]

\[=2\times 2\times 3\frac{1}{5}=\frac{12}{5}\]