Taking ‘a’, ‘b’ and ‘c’ outside the determinant from 1^st,2^nd and 3^rd column respectively

Taking ‘a’, ‘b’ and ‘c’ outside the determinant from 1^st,2^nd and 3^rd row respectively

.

R1 → R1 + R2 (i.e. Replacing 1^st row by addition of 1^st and 2^nd row)

panding the determinant along 1^st row

∴ LHS = a² b² c² × 2(1 - (-1)) = 4a²b²c² = RHS

∴