A) Statement-1 is true, Statement-2 is true; Statement -2 is not a correct explanation for Statement-1.
B) Statement-1 is true, Statement-2 is false.
C) Statement-1 is false, Statement-2 is true.
D) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
Correct Answer: B
Solution :
Let \[A=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]\] \[{{A}^{2}}=I\Rightarrow {{a}^{2}}+bc=1,\,bc+{{d}^{2}}=1,\,\] \[\,\left( a+b \right)b=0,\,\left( a+b \right)c=0\] Out of all possible matrices if we consider \[A=\left[ \begin{matrix} 1 & 0 \\ 0 & -1 \\ \end{matrix} \right]\], then tr A = 0. \[\Rightarrow \] Statement-2 is wrong. Again if \[A\ne \pm I\], then \[\left| A \right|=-1\] \[\Rightarrow \] Statement-1 is correct.You need to login to perform this action.
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