Suppose `A` and `B` are two non singular matrices such that `B != I, A^6 = I` and `AB^2 = BA`. Find the least value of `k` for `B^k = 1`

Explanation

To solve the problem, we need to find the least value of \( k \) such that \( B^k = I \), given the conditions \( A^6 = I \) and \( AB^2 = BA \).

### Step-by-Step Solution:

1. **Given Information**:
- \( A^6 = I \) (the identity matrix)
- \( AB^2 = BA \) (commutativity condition)
- \( B \neq I \) (B is not the identity matrix)
...