Question

Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of A² is 1, then the possible number of such matrices is

(1) 4

(2) 1

(3) 6

(4) 12

Answer 1

Correct option is (1) 4

Sum of the diagonal entries of

A² = a² + 2b² + c²

Given a² + 2b² + c² = 1, a, b, c ∈ I

b = 0 & a² + c² = 1

Case–1 : a = 0 ⇒ c = ±1 (2-matrices)

Case-2 : c = 0 ⇒ a = ±1 (2-matrices)
Total = 4 matrices