Given:

and it satisfies the matrix equation A⁴ = λA

Firstly, we find the A⁴

= 2 A

So, A⁴ = A² × A²

⇒ A⁴ = 2A × 2A

⇒ A⁴ = 4A²

⇒ A⁴ = 4 × 2A [∵A² = 2A]

⇒ A⁴ = 8A

∴ λ = 8

Hence, the value of λ = 8