Let A be a 2×2 real matrix with entries... | Matrices

JEE Main 2020

02-09-2020 S1

Question

Let $A$ be a $2 \times 2$ real matrix with entries from $\{0,1\}$ and $|A| \neq 0$. Consider the following two statements: (P) If $A \neq I_2$, then $|A|=-1$ (Q) If $|A|=1$, then $\operatorname{tr}(A)=2$, where $I_2$ denotes $2 \times 2$ identity matrix and $\operatorname{tr}(A)$ denotes the sum of the diagonal entries of $A$. Then:

Select the correct option:

(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

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution