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?
