Mathematics · 2013
JEE Main · 23 April 2013, Shift 1 · Q85
Let A, other than I or - I, be a 2 × 2 real matrix such that A^2= I, I being the unit matrix. Let Tr ( A ) be the sum of diagonal elements of A.…
Let A, other than I or - I, be a $\displaystyle 2 \times 2$ real matrix such that $\displaystyle \mathrm{A}^2=\mathrm{I}, \mathrm{I}$ being the unit matrix. Let $\displaystyle \operatorname{Tr}(\mathrm{A})$ be the sum of diagonal elements of A.Statement $\displaystyle 1$ : $\displaystyle \operatorname{Tr}(\mathrm{A})=0$ Statement $\displaystyle 2$ : $\displaystyle \operatorname{det}(\mathrm{A})=-1$
Official answer
(2)
Statement - $\displaystyle 1$ is true ; Statement - $\displaystyle 2$ is true ; Statement - $\displaystyle 2$ is not a correct explanation for Statement - 1.
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JEE Main 2013 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.