|A| =

We know that determinant of A is calculated as

= 1(2) - 2(4)

= 2 - 8

|A| = -6

LHS: |2A|

= 2(4) - 4(8)

= 8 - 32 = -24

|2A| = -24 …LHS

RHS: 4|A|

4|A|= 4(-6)

= -24

4|A| = -24 …RHS

LHS = RHS

Hence proved.