linear algebra - eigenvalues of symmetric matrix

Suppose we have $n \times n$ symmetric matrix $A$ with all diagonal entries zero and remaining entries are non negative. Let $B$ be the matrix obtained from $A$ by deleting its $k$th row and $k$th column and remaining entries of $B$ are less equal the corresponding entries of $A$. Then the largest eigenvalue of $B$ is less equal the largest eigenvalue of $A$ and the smallest eigenvalue of $A$ is less equal the smallest eigenvalue of $B$.