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 :

Option D. Let A = …\left[ {\matrix{ a & b \cr c & d \cr

Matrices and Determinants

JEE Main 2020 · 2 Sep, Morning shift · Q4653

MathematicsMedium244×since 2002Q4653

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 :