Question

Given that, for some a, b, c, d, e, f, g, h, i ∈ R, [a b c d e f g h i ] = 5, evaluate the following determinants:

(c) [ka ld mg

kb le mh

kc lf mi] Here, k, l, and m are non-negative constants.

Answer 1

Here, basically we use some basic properties of the determinants .

Determinant of matrix has a property that:

" Determinant of any matrix is equal to determinant of its transpose."

Thus, desired determinant is 5klm.