## Elementary Linear Algebra 7th Edition

The set $W$ of all $n \times n$ matrices with integer entries is not a vector subspace of $M_{n,n}$.
The set $W$ of all $n \times n$ matrices with integer entries is not a vector subspace of $M_{n,n}$. Because multiplying a matrix with integer entries, for example, by $\frac{1}{2}$ not necessarily yield a matrix with integer entries. So $W$ is not closed under scalar multiplication.