A) Zero matrix
B) Unit matrix
C) Symmetric matrix
D) Skew symmetric matrix
Correct Answer: D
Solution :
\[{{\log }_{x}}y{{\log }_{y}}x=1\}\] is a square matrix. For a skew symmetric matrix \[\left| \,\begin{matrix} x+4 & -1+x & 2 \\ 0 & -x & x \\ 0 & -x & 0 \\ \end{matrix}\, \right|\,=0\] Þ \[(x+4)\,(0+{{x}^{2}})=0\Rightarrow x=-4,\,0\] and \[{{a}_{ji}}={{j}^{2}}-{{i}^{2}}\] Þ \[{{a}_{ij}}+{{a}_{ji}}=0\Rightarrow \,{{a}_{ij}}=-{{a}_{ji}}\]. Hence, \[{{p}^{-1}}+I+Ip+............+{{p}^{n-1}}I=O.{{p}^{-1}}\] is a skew symmetric matrix.
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