Triangular Matrix Invertion

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$\left(\begin{array}{cccccc}1&0&0&0&0&0\\ a_{\mathrm{21}}/a_{\mathrm{11}}&1&0&0&0&0\\ a_{\mathrm{31}}/a_{\mathrm{11}}&a_{\mathrm{32}}/a_{\mathrm{22}}&1&0&0&0\\ a_{\mathrm{41}}/a_{\mathrm{11}}&a_{\mathrm{42}}/a_{\mathrm{22}}&a_{\mathrm{43}}/a_{\mathrm{33}}&1&0&0\\ a_{\mathrm{51}}/a_{\mathrm{11}}&a_{\mathrm{52}}/a_{\mathrm{22}}&a_{\mathrm{53}}/a_{\mathrm{33}}&a_{\mathrm{54}}/a_{\mathrm{44}}&1&0\\ a_{\mathrm{61}}/a_{\mathrm{11}}&a_{\mathrm{62}}/a_{\mathrm{22}}&a_{\mathrm{63}}/a_{\mathrm{33}}&a_{\mathrm{64}}/a_{\mathrm{44}}&a_{\mathrm{65}}/a_{\mathrm{55}}&1\end{array}\right)$

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$\notag \left[\begin{array}{crrrr} 1 & -\theta & -\theta & -\theta & -\theta\\ & 1 & -\theta & -\theta & -\theta\\ & & 1 & -\theta & -\theta\\ & & & 1 & -\theta\\ & & & & 1 \end{array}\right]^{-1} = \left[\begin{array}{ccccc} 1 & \theta & \theta(1+\theta) & \theta(1+\theta)^2 & \theta(1+\theta)^3\\ & 1 & \theta & \theta(1+\theta) & \theta(1+\theta)^2\\ & & 1 & \theta & \theta(1+\theta)\\ & & & 1 & \theta\\ & & & & 1 \end{array}\right]$

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