Using properties of determinants, prove that `|-a^2a b a c b a-b^2b cc a c b-c^2|=4a^2b^2c^2`

Explanation

LHS=

`=[[-a^2,ab,ac],[ba,-b^2,bc],[ca,cb,-c^2]]`

`=abc[[-a,b,c],[a,-b,c],[a,b,-c]]`

`=a^2b^2c^2[[-1,1,1],[1,-1,1],[1,1,-1]]`

`=a^2b^2c^2(2)[[1,-1],[1,1]]`

`=2a^2b^2c^2(1-(-1))`

`4a^2b^2c^2=RHS.