Question

If A is a 3 x 3 non singular matrix and
|A| = 3 then |(2A)-'| =
(A) 1/6
(B) 1/24
(C) 1 / 12
(D) None of these

Answer 1

Answer:

det(2A^-1) = 1 / 24

Step-by-step explanation:

We know that

If A is n x n matrix then

det(kA) = k^n (det(A))

And

det(A^-1) = 1 / det(A)

So

If A is the matrix such that

det(A) = 3

Then

det(2A^-1) = 1 / det(2A) = 1 / 2³ det(A)

Putting det(A) = 3 we get

det(2A^-1) = 1 / 8(3) = 1 / 24

Hence

det(2A^-1) = 1 / 24