WBJEE · Maths · Determinants
Let \(A\) and \(B\) are orthogonal matrices and \(\operatorname{det} A+\operatorname{det} B=0\). Then
- A \(A+B\) is singular
- B \(A+B\) is non-singular
- C \(A+B\) is orthogonal
- D \(A+B\) is skew symmetric
Answer & Solution
Correct Answer
(A) \(A+B\) is singular
Step-by-step Solution
Detailed explanation
Hint: \(A A^{\top}=I\) and \(B B^{\top}=I\) \(\Rightarrow \operatorname{det}\left(A A^{\top}\right)=1\) and \(\operatorname{det}\left(B B^{\top}\right)=1\) \(\operatorname{det}(A)=-\operatorname{det}(B)\) (Given)…
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