Question

If A, B are two square matries, such that AB = B, BA = A and n ∈ N then (A + B)ⁿ =

Options

• 2ⁿ(A + B)

• 2^n-1(A + B)

• 2ⁿ⁺¹(A + B)

• 2^n/2(A + B)

Answer 1

2ⁿ(A + B)

Explanation:

`(A + B)^n = sum_(n = 0)^n  n_(cr) A^(n - r) B^r`

Since A² = A, B² = B

= 2ⁿ(A + B)