A) \[-1\]
B) \[0\]
C) \[4\]
D) \[1\]
Correct Answer: B
Solution :
Given, M is a \[3\times 3\]skew symmetric matrix. Let \[M=\left[ \begin{matrix} 0 & -a & -b \\ a & 0 & -c \\ b & c & 0 \\ \end{matrix} \right]\] Then, \[\det \,(M)=0\left| \begin{matrix} 0 & -c \\ c & 0 \\ \end{matrix} \right|+a\left| \begin{matrix} a & -c \\ b & 0 \\ \end{matrix} \right|-b\left| \begin{matrix} a & 0 \\ b & c \\ \end{matrix} \right|\] \[\Rightarrow \] \[\det \,(M)=a(0+bc)-b(ac-0)\] \[=abc-abc\] \[\Rightarrow \] \[\det \,(M)=0\]
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