Let A=[acbd] so that A2=[a2+bcac+dcab+bdbc+d2]=[1001] ⇒a2+bc=1=bc+d2 and (a+d)c=0=(a+d)b. Since A=I,A=1,a=−d and hence detA=1−bccb−1−bc=−1+bc−bc=−1 Statement 1 is true. But tr. A=0 and hence statement 2 is false.
JEE Main 2008 — Mathematics Algebra
Let A be a 2×2 matrix with real entries. Let I be the 2×2 identity matrix. Denote by tr(A), the sum of diagonal entries of A. Assume that A2=1. Statement -1: If A=1 and A=−1, then detA=−1. Statement −2 : If A=1 and A=−1, then tr(A)=0.
Held on 30 Apr 2008 · Verified 6 Jul 2026.
Statement −1 is false, Statement −2 is true
Statement −1 is true, Statement −2 is true, Statement −2 is a correct explanation for Statement −1
Statement −1 is true, Statement −2 is true; Statement −2 is not a correct explanation for Statement −1
Statement −1 is true, Statement −2 is false.
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