Let A and B be 3 * 3 matrices, with det(A) = 2, det(B) = 3.

Question

Then det(5 A B^{-1}) =
a) none of these
b) 30
c) 250/3
d) 10/3
e) 2/3

Answer 1

since
|B^-1| = 1/|B|,
|AB| = |A|*|B|
|nA| = n^2 |A|,
the results is
5 * 2 * 1/3 = 10/3

Better study up some more on properties of determinants.

Answer 2

Actually
|nA| = n^3 |A| because it is a 3*3 matrix.

Seems like you better study up some more on properties of determinants