Using properties of determinants prove that:
[R1’ = R1 + R2]
[R1’ = R1/(a + b)]
[R2’ = R2 + R3]
[R2’ = R1/(b + c)]
= (a + b)(b + c){0 + 2( - b + a + b + c) + 0} [expansion by first row]
= 2(a + b)(b + c)(c + a)