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)=1, then tr(A)=-1
(Q) If(A)=1, then tr(A)=2
Where I2 denotes 2×2 identify matrix and tr(A) denotes the some of diagonal entries of A. Then

Answer 1

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 Read more on Sarthaks.com - https://www.sarthaks.com/902846/let-a-be-a-2-2-real-matrix-with-entries-from-0-1-and-a-0-consider-the-following-two-statements