Let $\mathrm{A}=\left[\begin{array}{cc}\alpha & \beta \ \gamma & -\alpha\end{array} ight]$ and $\m

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Let $\mathrm{A}=\left[\begin{array}{cc}\alpha & \beta \ \gamma & -\alpha\end{array}ight]$ and $\mathrm{I}=\left[\begin{array}{ll}1 & 0 \ 0 & 1\end{array}ight]$. If $\mathrm{A}^{2}-\mathrm{I}=\mathrm{O}$ then\

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$(b) \mathrm{A}=\left[\begin{array}{cc}\alpha & \beta \ \gamma & -\alpha\end{array}ight]$\ $\mathrm{I}=\left[\begin{array}{ll}1 & 0 \ 0 & 1\end{array}ight]$\ $A^{2}-I=0$\ $A^{2}=\left[\begin{array}{cc}\alpha & \beta \ \gamma & -\alpha\end{array}ight]\left[\begin{array}{cc}\alpha & \beta \ \gamma & -\alpha\end{array}ight]=\left[\begin{array}{cc}\alpha^{2}+\beta \gamma & \alpha \beta-\alpha \beta \ \alpha \gamma-\alpha \gamma & \gamma \beta+\alpha^{2}\end{array}ight]$\ $=\left[\begin{array}{cc}\alpha^{2}+\beta^{2} & 0 \ 0 & \gamma \beta+\alpha^{2}\end{array}ight]$\ $A^{2}-I=0\left[\begin{array}{cc}\alpha^{2}+\beta \gamma & 0 \ 0 & \gamma \beta+\alpha^{2}\end{array}ight]-\left[\begin{array}{ll}1 & 0 \ 0 & 1\end{array}ight]$\ $\left[\begin{array}{cc}\alpha^{2}+\beta \gamma-1 & 0 \ 0 & \gamma \beta+\alpha^{2}-1\end{array}ight]$\ $\left[\alpha^{2}+\beta \gamma-1ight]^{2}=0$\