jee-advanced 2022 Q16

jee-advanced · India · paper2 3 marks Matrices Matrix Power Computation and Application
If $M = \left( \begin{array} { r r } \frac { 5 } { 2 } & \frac { 3 } { 2 } \\ - \frac { 3 } { 2 } & - \frac { 1 } { 2 } \end{array} \right)$, then which of the following matrices is equal to $M ^ { 2022 }$ ?
(A) $\quad \left( \begin{array} { r r } 3034 & 3033 \\ - 3033 & - 3032 \end{array} \right)$
(B) $\quad \left( \begin{array} { l l } 3034 & - 3033 \\ 3033 & - 3032 \end{array} \right)$
(C) $\quad \left( \begin{array} { r r } 3033 & 3032 \\ - 3032 & - 3031 \end{array} \right)$
(D) $\quad \left( \begin{array} { r r } 3032 & 3031 \\ - 3031 & - 3030 \end{array} \right)$
If $M = \left( \begin{array} { r r } \frac { 5 } { 2 } & \frac { 3 } { 2 } \\ - \frac { 3 } { 2 } & - \frac { 1 } { 2 } \end{array} \right)$, then which of the following matrices is equal to $M ^ { 2022 }$ ?

(A) $\quad \left( \begin{array} { r r } 3034 & 3033 \\ - 3033 & - 3032 \end{array} \right)$\\
(B) $\quad \left( \begin{array} { l l } 3034 & - 3033 \\ 3033 & - 3032 \end{array} \right)$\\
(C) $\quad \left( \begin{array} { r r } 3033 & 3032 \\ - 3032 & - 3031 \end{array} \right)$\\
(D) $\quad \left( \begin{array} { r r } 3032 & 3031 \\ - 3031 & - 3030 \end{array} \right)$