Let $\mathbf{A}=\begin{bmatrix} 1 & \tfrac{1}{51} \\[2pt] 0 & 1 \end{bmatrix}$. If $\mathbf{B}=\begin{bmatrix} 1 & 2 \\ -1 & -1 \end{bmatrix}\mathbf{A}\begin{bmatrix} -1 & -2 \\ 1 & 1 \end{bmatrix}$, then the sum of all the elements of the matrix $\displaystyle \sum_{n=1}^{50} \mathbf{B}^n$ is equal to: