Using properties of determinants prove that:
[R1’ = R1 + R2 + R3]
[R1’ = R1/2]
[R1’ = R1 - R2]
= 2[c2{(c2 + a2)(a2 + b2) - b2c2} + 0 + a2{b2c2 - c2(c2 + a2)}] [expansion by first row]
= 2[c2(c2a2 + a4 + b2c2 + a2b2 - b2c2) + a2(b2c2 - c4 - a2c2)]
= 2[a2c4 + a4c2 + a2b2c2 + a2b2c2 - a2c4 - a4c2]
= 4a2b2c2
1