Let A be a 2 × 2 matrix with real entries. Let I be the 2 × 2 identity matrix. Denote by tr (A), the sum of diagonal entries of A. Assume that A2 = I.

Statement −1: If A ≠ I and A ≠ − I, then det A = − 1.

Statement −2: If A ≠ I and A ≠ − I, then tr (A) ≠ 0.