A) Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement -1
B) Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.
C) Statement -1 is true, Statement -2 is false.
D) Statement -1 is false, Statement -2 is true.
Correct Answer: C
Solution :
Let \[\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]\] \[{{A}^{2}}=I\] \[\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] \[\left[ \begin{matrix} {{a}^{2}}+bc & ab+bd \\ ac+dc & bc+{{d}^{2}} \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] \[ab+bd=0\] \[b(a+d)=0\] \[b\ne 0\] so, \[a=d\] \[A=\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]\] \[a+b=0\] \[{{T}_{r}}(A)=0\] But \[|A|\ne 1.\] So, statement I is true and statement 2 is false.You need to login to perform this action.
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