Question

A and B are invertible matrices of the same order such that |(AB)^-1| = 8, If |A| = 2, then |B| is ____________.

Options

• 16

• 4

• 6

• `1/16`

Answer 1

A and B are invertible matrices of the same order such that |(AB)^-1| = 8, If |A| = 2, then |B| is `underline(1/16)`.

Explanation:

as `abs (("AB")^-1) = 1/abs("AB") = 1/(abs("A")abs ("B"))`

`=> 8 = 1/(2 abs"B") => "B" = 1/16`