Recently, I met a problem related to p-adic matrices in my research, the key of the problem can be summarized in the following way: 1: whether there exist spectrum theorem for p-adic matrix.\
2: whether invertible p-adic matrix is dense in $C_{p}^{n\times n}$
3:whether diagonalizable p-adic matrix is dense in $C_{p}^{n\times n}$, i.e. for almost every matrix $V \in C_{p}^{n \times n} $, there exist invertible $P$, $P^{-1}VP$ is a diagonalizable matrix.
Any reference and comments will be appreciated.