Answer:
Let A be a skew-symmetric matrix of order n. Then, \[A'=-A\] \[\Rightarrow \] \[|A'|\,\,=\,\,|-\,A|\] \[\Rightarrow \] \[|A'|\,\,={{(-1)}^{n}}|A|\] \[\Rightarrow \] \[|A'|\,\,=-|A|\] [\[\because \] n is odd] \[\Rightarrow \] \[|A|\,\,=-|A|\] \[[\because \,\,\,|A'|\,\,=-|A|]\] \[\Rightarrow \] \[2|A|\,\,=0\] \[\Rightarrow \] \[|A|\,\,=0\] Hence, determinant value of a skew-symmetric matrix of odd order is always zero.
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