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