KCET · Maths · Determinants
If a matrix \( \mathrm{A} \) is both symmetric and skewsymmetric, then
- A \( A \) is diagonal matrix
- B \( \mathrm{A} \) is a zero matrix
- C \( \mathrm{A} \) is scalar matrix
- D \( A \) is square matrix
Answer & Solution
Correct Answer
(B) \( \mathrm{A} \) is a zero matrix
Step-by-step Solution
Detailed explanation
For symmetric matrix, we know that:
\(A^{T}=A \rightarrow(1)\)
For skew-symmetric matrix, we know that:
\(A^{T}=-A \rightarrow(2)\)
So, \(A=-A \Rightarrow A=0\)
Therefore, matrix \(\mathrm{A}\) is a zero matrix.
\(A^{T}=A \rightarrow(1)\)
For skew-symmetric matrix, we know that:
\(A^{T}=-A \rightarrow(2)\)
So, \(A=-A \Rightarrow A=0\)
Therefore, matrix \(\mathrm{A}\) is a zero matrix.
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