Let A=[acbd]a,b,c,d∈0,1
∣A∣=ad−bc=0
⇒ad=1,bc=0 or ad=0,bc=1
(P)
If A=I2⇒ad=1⇒ad=0,bc=1⇒∣A∣=−1
(P) is true.
(Q)
If ∣A∣=1⇒ad=1,bc=0⇒tr(A)=2
(Q) is true.
Let A be a 2×2 real matrix with entries from 0,1 and ∣A∣=0. Consider the following two statements;
(P) If A=l2, then ∣A∣=−1
(Q) If ∣A∣=1, then tr(A)=2
Where l2 denotes 2×2 identity matrix and tr(A) denotes the sum of the diagonal entries of A. Then
Held on 2 Sept 2020 · Verified 6 Jul 2026.
(P) is false and (Q) is true
Both (P) and (Q) are false
(P) is true and (Q) is false
Both (P) and (Q) are true
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