A) Statement 1 is true; Statement 2 is false.
B) Statement 1 is true; Statement 2 is true; Statement 2 is not correct explanation for Statement 1.
C) Statement 1 is true; Statement 2 is true; Statement 2 is a correct explanation for Statement 1.
D) Statement 1 is false; Statement 2 is true.
Correct Answer: B
Solution :
\[\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]\left[ \begin{matrix} a & b \\ c & d \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] \[\left[ \begin{matrix} {{a}^{2}}+bc & ab+bd \\ ac+cd & bc+{{d}^{2}} \\ \end{matrix} \right]=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right]\] \[b(c+d)=0,b=0\]or\[a=-d\] ?(1) \[c(a+d)=0,c=0\]or\[a=-d\] ?(2) \[{{a}^{2}}+bc=1,bc+{{d}^{2}}=1\] ?(3) 'a' and 'd? are diagonal elements a + d = 0 statement-1 is correct. Now, det =ad-bc Now, from(3) \[{{a}^{2}}+bc=1\]and\[{{d}^{2}}+bc=1\] So,\[{{a}^{2}}+{{d}^{2}}=0\] Adding \[{{a}^{2}}+{{d}^{2}}+2bc=2\] \[={{(a+d)}^{2}}-2ad+2bc=2\] or\[0-2(ad-bc)=2\] So,\[ad-bc=1\Rightarrow \det (A)=-1\] So, statement - 2 is also true. But statement - 2 is not the correct explanation of statement-I
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