KCET · Maths · Determinants
If \(A\) and \(B\) are square matrices of same order and \(B\) is a skew symmetric matrix, then \(A^{\prime} B A\) is
- A Symmetric matrix
- B Null matrix
- C Diagonal matrix
- D Skew symmetric matrix
Answer & Solution
Correct Answer
(D) Skew symmetric matrix
Step-by-step Solution
Detailed explanation
Given \(B\) is skew-symmetric matrix
\(\begin{gathered}
\therefore \quad B^{\prime}=-B \\
\left(A^{\prime} B A\right)^{\prime}=A^{\prime} B^{\prime} A=A^{\prime}(-B) A=-\left(A^{\prime} B A\right)
\end{gathered}\)
\(\therefore A^{\prime} B A\) is skew symmetric matrix.
\(\begin{gathered}
\therefore \quad B^{\prime}=-B \\
\left(A^{\prime} B A\right)^{\prime}=A^{\prime} B^{\prime} A=A^{\prime}(-B) A=-\left(A^{\prime} B A\right)
\end{gathered}\)
\(\therefore A^{\prime} B A\) is skew symmetric matrix.
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