99 Percentile Qs Bank for JEE MainMathematicsMatrices
Let A = 1 6 - 1 3 - 1 6 - 1 3 2 3 1 3 - 1 6 1 3 1 6 . If A 2016 l + A 2017 m + A 2018 n = 1 α A , for every l ,   m ,   n ∈ N , then the value of α is
Options
- A1 6
- B1 3
- C1 2
- D2 3
Correct answer
B. 1 3
Step-by-step solution
A = 1 6 - 1 3 - 1 6 - 1 3 2 3 1 3 - 1 6 1 3 1 6 ⇒ A 2 = A × A = 1 6 - 1 3 - 1 6 - 1 3 2 3 1 3 - 1 6 1 3 1 6 × 1 6 - 1 3 - 1 6 - 1 3 2 3 1 3 - 1 6 1 3 1 6 = 1 36 6 - 12 - 6 - 12 24 12 - 6 12 6 = 6 36 1 - 2 - 1 - 2 4 2 - 1 2 1 = 1 6 - 2 6 - 1 6 - 2 6 4 6 2 6 - 1 6 2 6 1 6 A 2 = A ∴   A 2016 l = A ,   A 2017 m = A ,   A 2018 n = A LHS :   A + A + A = 3 A RHS :   1 α A ∴   α = 1 3