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 :

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 :

(P) is true and (Q) is false

Both (P) and (Q) are false

Both (P) and (Q) are true

(P) is false and (Q) is true

Solution

Please login to view the detailed solution steps...

Go to DASH