Question

Let A and B are two square matrices of order 3 such that det. `(A)=3` and det. `(B)=2`, then the value of det. `(("adj. "(B^(-1) A^(-1)))^(-1))` is equal to _______ .

Answer 1

Correct Answer - 36
`("adj. "(B^(-1) A^(-1)))^(-1)=("adj. "(AB)^(-1))^(-1)`
`=(("adj. "(AB))^(-1))^(-1)" "["as adj. "A^(-1)=("adj. A")^(-1)]`
= adj. (AB)
`:. |("adj. (AB)")|=|AB|^(2)=|A|^(2)|B|^(2)=9xx4=36`