JEE Main 2026 — 6 April, Evening Shift — Question 25

$\mathrm{A}=\mathrm{P}+\mathrm{I}$ $A=\left[\begin{array}{lll}0 & 0 & 0\\ 3 & 0 & 0\\ 9 & 3 & 0\end{array}\right]+\left[\begin{array}{lll}1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\end{array}\right]$ $\mathrm{A}=\mathrm{P}+\mathrm{I}$ where $\mathrm{P}^{3}=0$ $\mathrm{A}^{99}=\mathrm{I}+99 \mathrm{P}+{ }^{99} \mathrm{C}_{2} \mathrm{P}^{2}$ $\mathrm{A}^{99}-\mathrm{I}=99\left[\begin{array}{lll}0 & 0 & 0\\ 3 & 0 & 0\\ 9 & 3 & 0\end{array}\right]+{ }^{99} \mathrm{C}_{2}\left[\begin{array}{lll}0 & 0 & 0\\ 0 & 0 & 0\\ 9 & 0 & 0\end{array}\right]$ $=\left[\begin{array}{ccc}0 & 0 & 0\\ 99 \times 3 & 0 & 0\\ 44550 & 99 \times 3 & 0\end{array}\right]$ $\mathrm{b}_{31}=44550, \mathrm{~b}_{21}=99 \times 3, \mathrm{~b}_{32}=99 \times 3$ $\frac{44550-297}{297}=149$