If $M=\left[\begin{array}{ll}1& 2\\ 2& 3\end{array}\right]$ and $M^{\mathit{2}}\mathit{-}\lambda M\mathit{-}{I}_{\mathit{2}}\mathit{=}O$, then $\mathrm{\lambda }$ equals -

Let three matrices $A=\left[\begin{array}{ll}2& 1\\ 4& 1\end{array}\right]; B=\left[\begin{array}{ll}3& 4\\ 2& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}3& -4\\ -2& 3\end{array}\right]$ then

$t_{\mathrm{r}}\left(\mathrm{A}\right)+t_{\mathrm{r}}\left(\frac{ABC}{2}\right)+t_{\mathrm{r}}\left(\frac{A(BC{)}^2}{4}\right)+{\mathrm{t}}_{\mathrm{r}}\left(\frac{A(BC{)}^3}{8}\right)+\dots \dots +\infty =$