Let A = [3, -4; 1, -1] and B be two matrices such that A^100=100 B + I. Then the sum of all the elements of B^100 is ____

Let $\displaystyle \mathrm{A}=\left[\begin{array}{ll}3 & -4 \\ 1 & -1\end{array}\right]$ and B be two matrices such that $\displaystyle \mathrm{A}^{100}=100 \mathrm{~B}+\mathrm{I}$. Then the sum of all the elements of $\displaystyle \mathrm{B}^{100}$ is $\displaystyle \_\_\_\_$