Determinant of matrix

Given that the determinant of that matrix [[1 3 0] [2 6 4] [-1 0 2]] (Consider it row wise) is -12. the determinant of the matrix [[2 6 0] [4 12 8] [-2 0 4]].

Solution : Let’s suppose A= [[1 3 0] [2 6 4] [-1 0 2]] and B = [[2 6 0] [4 12 8] [-2 0 4]].

So find the first mode of A (|A|) =1(12–0) — 3(4 + 4) + 0 = -12 .

|B| = |2 A| ( if you multiple with 2 in A you will get B matrix).

|B| = |2||A| (rule: |AB| = |A||B|)

|B| = (2)n |A| (here (2)n = 2 rest to n)

|B| = (2)3 (-12) ( here dimension of matrix n = 3 and |A| = -12 )

|B| = 8 (-12)

|B| = -96

So Answer of [[2 6 0] [4 12 8] [-2 0 4]] is -96.