Question
माना $M =\left[\begin{array}{cc}0 & -\alpha \\ \alpha & 0\end{array}\right]$ है, जहाँ $\alpha$ अशून्य वास्तविक तथा $N =\sum \limits_{ k =1}^{49} M ^{2 k }$ है। यदि $\left( I - M ^2\right) N =-2 I$ है, तो $\alpha$ का धनात्मक पूर्णांक मान है।
$N = M ^{2}+ M ^{4}+\ldots \ldots+ M ^{98}=\left[-\alpha^{2}+\alpha^{4}-\alpha^{6}+\ldots .\right] I$
$=-\alpha^{2} \frac{\left(1-\left(-\alpha^{2}\right)^{49}\right)}{1+\alpha^{2}} . I$
$I - M ^{2}=\left(1+\alpha^{2}\right) I$
$\left( I - M ^{2}\right) N =-\alpha^{2}\left(\alpha^{98}+1\right)=-2$
$\alpha=1$
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