JEE Math Practice Question

Let A be a 2 $$ \times $$ 2 real matrix with entries from {0, 1} and |A| $$ \ne $$ 0. Consider the following two statements : (P) If A $$ \ne $$ I2 , then |A| = –1 (Q) If |A| = 1, then tr(A) = 2, where I2 denotes 2 $$ \times $$ 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then :

1. A.(P) is true and (Q) is false
2. B.Both (P) and (Q) are false
3. C.Both (P) and (Q) are true
4. D.(P) is false and (Q) is true