Question

If AB = A, BA = B then (A + B)ⁿ = (Where \(n \in N\))
1. A² + B²)
2. (A + B)
3. A + B
4. 2^{n - 1} (A + B)

Answer 1

Correct Answer - Option 4 : 2^{n - 1} (A + B)

(A + B)² = A² + AB + BA + B²

= 2(A + B)

(A + B)³ = 2 (A + B) (A + B) = 2² (A + B)

(A + B)ⁿ = 2^{n - 1}(A + B)