JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) and \(B\) be two \(3 \times 3\) real matrices such that \(\left(A^{2}-B^{2}\right)\) is invertible matrix. If \(A^{5}=B^{5}\) and \(A^{3} B^{2}=A^{2} B^{3}\), then the value of the determinant of the matrix \(A^{3}+B^{3}\) is equal to:
- A \(0\)
- B \(2\)
- C \(1\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(0\)
Step-by-step Solution
Detailed explanation
\(C=A^{2}-B^{2} ;|C| \neq 0\) \(A^{5}=B^{5}\) and \(A^{3} B^{2}=A^{2} B^{3}\) Now, \(A^{5}-A^{3} B^{2}=B^{5}-A^{2} B^{3}\) \(\Rightarrow A^{3}\left(A^{2}-B^{2}\right)+B^{3}\left(A^{2}-B^{2}\right)=0\) \(\Rightarrow\left(A^{3}+B^{3}\right)\left(A^{2}-B^{2}\right)=0\) Post…
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