Let A be a 2 × 2 real matrix with entries from {0, 1} and \mathrm{|A|\neq0} Consider the following two statements :

(P) If \mathrm{A\neq I_2}, then |A| = –1

(Q) If |A| = 1, then tr(A) = 2,

where I2 denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then:
Option: 1 (P) is false and (Q) is true
Option: 2 Both (P) and (Q) are false
Option: 3 (P) is true and (Q) is false
Option: 4 Both (P) and (Q) are true

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