A) \[0\]
B) \[1\]
C) \[2\]
D) \[3\]
Correct Answer: A
Solution :
Given, \[A=\left[ \begin{matrix} 0 & -3 & -4/3 \\ 3 & 0 & -1/4 \\ 4/3 & 1/4 & 0 \\ \end{matrix} \right]\] \[\therefore \] \[{{A}^{T}}=\left[ \begin{matrix} 0 & 3 & 4/3 \\ -3 & 0 & 1/4 \\ -4/3 & -1/4 & 0 \\ \end{matrix} \right]\] Now, \[A+{{A}^{T}}=\left[ \begin{matrix} 0 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \\ \end{matrix} \right]\] \[\therefore \] \[\det \,(A+{{A}^{T}})=0\]
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