Do I have to multiply it whole? Given that $$A=\begin{bmatrix}4 & 1\\ -9 & -2 \end{bmatrix}$$
and $$A^{100}=\begin{bmatrix}a & b\\ c & d \end{bmatrix}$$
What is $a$?
I tried to multiply it again and again but it seems lengthy. Is there a shorter method?

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*Jewar, you give the green chevron to a proof which is not a proof; understanding mathematics is a long way...

*The good question would be: what is $A^{100}$ ?
Indeed $A=I_2+U$ where $U^2=0_2$. Then $A^k=I_2+k U$.
