A quick answer for this question?

Question

If A is a sequare matrix of order 3 and |A|=5 ,then |(2A)^-1| is equal to?

A)2/5

B)1/40

C)8/5

D)1/10

Answer 1

Matrix of Order 3 has determinant 5, as according to the question.

It is known that det(A)=1/det(A^-1)

It is also known that given some non-zero scalar 'c,' (c*A)^-1 is equal to c^-1*A^-1

Therefore, det((2A)^-1)= |.5*A^-1|

Another property of determinants, is that given a scalar multiplier in the determinant for a square matrix, we can remove it, by setting it to the power of n, where the matrix is an n X n matrix.

So our new value is .5³|A^-1|.

From our first statement, where det(A)= 1/det(A^-1), we can flip it, and find that det(A^-1)=1/det(A).

Now we have .5³(1/|A|), from |(2A)^-1|

We solve this equation with our knowns: .125*(1/5)=.025, which is 1/40.