Let `A= [[a,b,c],[p,q,r],[x,y,z]]` and suppose then det (A) = 2, then det (B) equals, where `B = [[4x,2a,-p],[4y, 2b, -q],[4z, 2c, -r]]`

Options

A. -2
B. -8
C. -16
D. 8

Answer

C

Explanation

`because det (B) = abs((4x, 2a, -p),(4y, 2b, -q),(4z, 2c, -r)) = -8 abs((x,a,p),(y,b,q),(z,c,r))`
`= -8 abs((x,y,z),(a,b,c),(p,q,r))= 8 abs((a,b,c),(x,y,z),(p,q,r))` [by property]
`= -8 abs((a,b,c),(p,q,r),(x,y,z)) =-8 det (A) = -16`