If B is a non-singular matrix and A is a square matrix, then `det (B^(-1) AB)` is equal to (A) `det (A^(-1))` (B) `det (B^(-1))` (C) `det (A)` (D) `det (B)`

Options

A. det (B)
B. det (A)
C. `det(B^(-1))`
D. `det(A^(-1))`

Answer

B

Explanation

`|B^(-1)AB|=|B^(-1)||A||B|`
`=(1)/(|cancel(B)|)|A||cancel(B)|" "because|B^(-1)|=(1)/(|B|)`
`=|A|`