JEE Main 2020 Mathematics question

Let A be a 2 × 2 real matrix with entries from {0, 1} and |A| ≠ 0. Consider the following two statements : (P) If A ≠ , then |A| = –1 (Q) If |A| = 1, then tr(A) = 2, where denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then:

• (A)(P) is true and (Q) is false
• (B)Both (P) and (Q) are false
• (C)Both (P) and (Q) are true
• (D)(P) is false and (Q) is trueCorrect