If the matrix A = α 0 2 α ∀ α ∈ R ,   α > 0 and 2 A 2 - 2 A = 144 , then the value of A + t r A is equal to (where t r A represent the trace of the matrix A i.e. the sum of all the principal diagonal elements of the matrix A and A is the determinant value of A )

Step-by-step solution

2 A 2 - 2 A = 144 2 2 A A - I = 144 ⇒ α 2 α - 1 2 = 36 α α - 1 = 6 or - 6 α 2 - α - 6 = 0 or α 2 - α + 6 = 0 α - 3 α + 2 = 0 or α = 1 ± 1 - 24 2 × 1 α = 3 or - 2 (rejected) or 1 2 ± i 23 2 (rejected) ∴ t r A = 2 α = 6 A = α 2 = 9 A + t r A = 15