Using the properties of determinants, prove that

.

To Prove:

Applying, R₁→ R₁ – R₂, we get,

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

Now, applying R₂→ R₂ – R₃, we get,

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

On expanding, we get,

= (a – 1)² [(a + 1)(1 – 0) – 1(2 – 0) + 0]

= (a – 1)² (a – 1)

= (a – 1)³ = R.H.S

Hence, Proved.