TS EAMCET · Maths · Matrices
If \(M\) and \(N\) are square matrices of order 3 , then which one of the following statements is not true?
- A For all symmetric matrices \(M\) and \(N, M N-N M\) is skew symmetric
- B \(N^{\top} M N\) is symmetric or skew symmetric according as \(M\) is symmetric or skew symmetric
- C For all symmetric matrices \(M\) and \(N\), matrix \(M N\) is symmetric
- D For any two matrices \(M\) and \(N\), adj \((M N)\) and adj (NM) need not be equal
Answer & Solution
Correct Answer
(C) For all symmetric matrices \(M\) and \(N\), matrix \(M N\) is symmetric
Step-by-step Solution
Detailed explanation
For two square matrices \(M\) and \(N\) of order 3 , the matrix \(M N-N M\) is skew symmetric, if \(M\) and \(N\) are symmetric matrices, because \(\begin{aligned} & (M N-N M)^T=(M N)^T-(N M)^T \\ & =N M-M N=-(M N-N M)\end{aligned}\) The matrix \(N^T M N\) is symmetric or skew…
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