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:

(D) (P) is false and (Q) is true

(A) (P) is true and (Q) is false

Matrices and Determinants: JEE Main 2020 Mathematics question

JEE Main 2020 · 2 Sep, Morning shift · Q4653

JEE Main 20202 Sep, Morning shiftMathematicsMediumMatrices and Determinants245× since 2002

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 :

JEE Main 2020 Matrices and Determinants Question with Solution (2 Sep Morning shift, Q4653) | JEE Arc