Using properties of determinants prove that:
[R2’ = R2 - R3]
[R2’ = R2/4]
[transforming row and column]
[R1’ = R1 - R2 & R2’ = R2 - R3]
[R1’ = R1/(a - b) & R2’ = R2/(b - c)]
[R1’ = R1 - R2]
[R1’ = R1/(a - c)]
= 4(a - b)(b - c)(a - c)(c2 - 2c + 1 - bc - c2 + 2c + 0 + bc + c2 - c2) [expansion by first row]
= 4(a - b)(b - c)(c - a)