Consider the matrix \[ M= \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \] Let \(p,q,r,s,a,b,c,d\) be integers such that \[ M^{26}= \begin{bmatrix} p & q \\ r & s \end{bmatrix} \] and \[ \sum_{k=1}^{26} M^k= \begin{bmatrix} a & b \\ c & d \end{bmatrix}. \] Then which of the following statements is (are) TRUE?
