A) 2
B) 0
C) 1
D) 3
Correct Answer: C
Solution :
Let\[A=\left( \begin{matrix} \alpha -1 \\ 0 \\ 0 \\ \end{matrix} \right),B=\left( \begin{matrix} \alpha +1 \\ 0 \\ 0 \\ \end{matrix} \right)\]be two matrices. \[A{{B}^{T}}=\left( \begin{matrix} \alpha -1 \\ 0 \\ 0 \\ \end{matrix} \right),(\alpha +1\,\,0\,\,\,0)\]\[\left( \begin{matrix} {{\alpha }^{2}}-1 \\ 0 \\ 0 \\ \end{matrix}\,\,\,\,\,\,\,\,\begin{matrix} 0 & 0 \\ 0 & 0 \\ 0 & 0 \\ \end{matrix} \right)\] Thus, \[A{{B}^{T}}\]is non-zero matrix for\[|\alpha |\ne 1\]
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