Digit Matrix

You are given a matrix $A$ of non-negative integers with $N$ rows (numbered $1$ through $N$) and $N$ columns (numbered $1$ through $N$). For each valid $i$ and $j$, let's denote the element in the $i$-th row and $j$-th column by $A_{i,j}$. You need to find a matrix $B$ with $N+1$ rows and $N+1$ columns (numbered similarly) such that: - each element of this matrix is a digit between $0$ and $9$