A) \[\det \,\,A=not\,\,exist\]
B) \[\det \,\,A=0\]
C) \[\det \,\,A=\pm 1\]
D) None of these
Correct Answer: C
Solution :
Since,\[A\]is an orthogonal matrix, therefore, \[AA=I\Rightarrow |A\cdot A|=|I|\Rightarrow |A|\cdot |A|=1\] \[\Rightarrow \] \[|A|\cdot |A|=1\] \[(\because |I|\,\,=1)\] \[\Rightarrow \] \[|A{{|}^{2}}=1\] \[(\because \,\,|A|=|A|)\] \[\Rightarrow \] \[|A|=\pm 1\]
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