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 ≠ I₂ , 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:

 (1) (P) is true and (Q) is false 

(2) Both (P) and (Q) are false 

(3) Both (P) and (Q) are true 

(4) (P) is false and (Q) is true

Answer 1

Answer is (4) (P) is false and (Q) is true

|A| ≠ 0

For (P) : A ≠ I₂

⇒ tr(A) = 2

⇒ Q is true