Let M=beginpmatrix1&2&0\\0&1&2\\0&0&1endpmatrix and let I be the identity matrix of order 3.

Write $M=I+N$ with $N=\begin{pmatrix}0&2&0\\0&0&2\\0&0&0\end{pmatrix}$, so $N^2$ has the single nonzero entry $4$ at position $(1,3)$ and $N^3=0$. Then $M^n=I+nN+\binom n2N^2$, whose $(1,3)$ entry is $4\binom n2=2n(n-1)$; for $n=10$ this is $180$, so (A) is true. $M$ has the single eigenvalue $1$ but $M\neq I$ (equivalently $N\neq0$), so it is not diagonalizable and (B) is false. $M^{-1}=I-N+N^2=\begin{pmatrix}1&-2&4\\0&1&-2\\0&0&1\end{pmatrix}$, whose $(1,3)$ entry is $4$, so (C) is true. The entries of $M^{-1}$ add to $3-2-2+4=3$, not $1$, so (D) is false. Answer: A and C.