If $A=\left(\begin{array}{c}\alpha-1 \ 0 \ 0\end{array} ight), B=\left(\begin{array}{c}\alpha+1 \ 0 \ 0\end{array} ight)$ be two matrices, then $A B^T$ is a non-zero matrix for $|\alpha|$ not equal to

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If $A=\left(\begin{array}{c}\alpha-1 \ 0 \ 0\end{array}ight), B=\left(\begin{array}{c}\alpha+1 \ 0 \ 0\end{array}ight)$ be two matrices, then $A B^T$ is a non-zero matrix for $|\alpha|$ not equal to

Aicharya · Accepted Answer

Let $A=\left(\begin{array}{c}\alpha-1 \ 0 \ 0\end{array}ight), B=\left(\begin{array}{c}\alpha+1 \ 0 \ 0\end{array}ight)$ be two matrices. $ \begin{aligned} & A B^T=\left(\begin{array}{c} \alpha-1 \ 0 \ 0 \end{array}ight)(\alpha+1 \quad 0 \quad 0) \ & =\left(\begin{array}{ccc} \alpha^2-1 & 0 & 0 \ 0 & 0 & 0 \ 0 & 0 & 0 \end{array}ight) \ & \end{aligned} $

If $A=\left(\begin{array}{c}\alpha-1 \\ 0 \\ 0\end{array}\right), B=\left(\begin{array}{c}\alpha+1 \\ 0 \\…

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