Taking LHS,

Applying R₁→ R₁ – R₂, we get

[∵(a² – b²) = (a – b)(a + b)]

Taking (a – 1) common from the first row, we get

Applying R₂→ R₂ – R₃, we get

Taking (a – 1) common from the second row, we get

Now, expanding along C₃, we get

= (a – 1)² [1{(a + 1) – 2}]

= (a – 1)² [a + 1 – 2]

= (a – 1)³

= RHS

Hence, LHS = RHS

Hence Proved