Question

If $A$ and $B$ are square matrices of order ' 3 ' such that $A$ adj $(2 B)=16 I _3$ and $\operatorname{det}(B)=2$ then which of the following is/are true (Where adj $( X )$ denotes adjoint of matrix $( X ), X ^{-1}$ denotes inverse of matrix $( X )$ ) and $\operatorname{det}( X )$ denotes determinant value of matrix $( X )$.

• A. $\left( A ^{-1}(\operatorname{adj}( B ))^{-1}=4 A ^2\right.$
• B. $\left(A^{-1}(\operatorname{adj}( B ))^{-1}= B ^2\right.$
• C. $B (\operatorname{adj} A )=8 I _3$
• D. $B(\operatorname{adj} A)=4 I_3$

Answer 1

Answer: (B), (C)

Correct answer is (b) $\left(A^{-1}(\operatorname{adj}( B ))^{-1}= B ^2\right.$Correct answer is (c) $B (\operatorname{adj} A )=8 I _3$