Let `A` be a `2xx3` matrix, whereas `B` be a `3xx2` amtrix. If `det.(AB)=4`, then the value of `det.(BA)` is

Options

A. `-4`
B. `2`
C. `-2`
D. `0`

Answer

D

Explanation

`(d)` Let `A=[{:(a_(1),a_(2),a_(3)),(a_(4),a_(5),a_(6)):}]`, `B=[{:(b_(1),b_(2)),(b_(3),b_(4)),(b_(5),b_(6)):}]`
So, det `(BA)=|{:(b_(1)a_(1)+b_(2)a_(4),,b_(1)a_(2)+b_(2)a_(5),,b_(1)a_(3)+b_(2)a_(6)),(b_(3)a_(1)+b_(4)a_(4),,b_(3)a_(2)+b_(4)a_(5),,b_(3)a_(3)+b_(4)a_(6)),(b_(3)a_(1)+b_(6)a_(4),,b_(5)a_(2)+b_(6)a_(5),,b_(5)a_(3)+b_(6)a_(6)):}|`
`=|{:(a_(1),,a_(2),,a_(3)),(a_(4),,a_(5),,a_(6)),(0,,0,,0):}|xx|{:(b_(1),,b_(2),,0),(b_(3),,b_(4),,0),(b_(5),,b_(6),,0):}|=0` (column by row)