What does the notation $M_n(\mathbb{Z})$ mean?

Question

In my literature it is stated that the matrix $A\in M_n(\mathbb{Z}).$ What does this mean?

Answer 1

In general the set $M_n(R)$ or $R^{n\times n}$ denotes the set of $n\times n$ square matrices with entries taken from the ring $R$. Addition and multiplication of matrices is done in the usual way with coefficients treated as members of $R$. So the set $M_n(\mathbb Z)$ denotes, as mentioned in the comments, the set of $n\times n$ matrices with integer entries.