If

Then find the value of .

We have,

Expanding it along R₁ to get,

1(a²×a – 1× 1) – a (a× a – a² × 1) + a² (a× 1 – a²× a²) = - 4

⇒ (a³ – 1) – a (a² – a²) + a² (a – a⁴) = - 4

⇒ (a³ – 1) – a (0) + a² (a – a⁴) = - 4

⇒ (a³ – 1) + a² (a – a⁴) = - 4

⇒ (a³ – 1) + a²× a (1 – a³) = - 4

⇒ (a³ – 1) + a³ (1 – a³) = - 4

⇒ (a³ – 1) - a³ (a³ - 1) = - 4

⇒ (a³ – 1) (1 - a³)= - 4

⇒ -(1 - a³)(1 - a³)= - 4

⇒ -(1 - a³)²= - 4

⇒ (1 - a³)²= 4 ….. (1)

Now in

Expand along R₁ to get,

= (a³ – 1) [ (a – a⁴) × 0 - (a³ – 1) (a³ – 1)] – 0[ 0 × 0 -(a – a⁴) (a³ – 1)] + (a – a⁴) [0× (a³ – 1)- (a – a⁴) (a – a⁴)]

= (a³ – 1) [ 0 - (a³ – 1)²] – 0[ 0 -(a – a⁴) (a³ – 1)] + (a – a⁴) [0 - (a – a⁴)²]

= - (a³ – 1)³ – (a – a⁴)³

= - (a³ – 1)³ – (a (1 – a³))³

= - (a³ – 1)³ – a³ (1 – a³)³

= - ((-1)³ (1 – a³))³ – a³ (1 – a³)³

= - (-1) (1 – a³))³ – a³ (1 – a³)³

= (1 – a³)³ – a³ (1 – a³)³

= (1 – a³)³ (1 – a³)

= (1 – a³)⁴

= ((1 - a³)²)²

From (1)

= (4)²

= 16