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JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
Let \(A\) and \(B\) be any two \(3 \times 3\) symmetric and skew symmetric matrices respectively. Then which of the following is \(NOT\) true?
- A \(A ^{4}- B ^{4}\) is a symmetric matrix
- B \(AB - BA\) is a symmetric matrix
- C \(B ^{5}- A ^{5}\) is a skew-symmetric matrix
- D \(AB + BA\) is a skew-symmetric matrix
Answer & Solution
Correct Answer
(C) \(B ^{5}- A ^{5}\) is a skew-symmetric matrix
Step-by-step Solution
Detailed explanation
Given that \(A^{T}=A, B^{T}=-B\) \(C =A^{4}-B^{4}\) \(C^{ T }=\left( A ^{4}- B ^{4}\right)=\left( A ^{4}\right)^{ T }-\left( B ^{4}\right)^{ T }= A ^{4}- B ^{4}= C\) \(C = AB - BA\) \(C ^{ T }=( AB - BA )^{ T }=( AB )^{ T }-( BA )^{ T }\)…
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