An interval matrix \(A_ I=(A_ c-\Delta,A_ c+\Delta)\) is called singular if it contains a singular matrix. Here, \(A_ c\) and \(\Delta\) are real \(n\times n\) matrices and \(\Delta\) nonnegative. It is shown that a singular interval matrix \(A_ I\) contains a singular matrix of a special type, i.e., \(A_ s=A_ c-dT_ y\Delta T_ x\) where \(0\leq d\leq 1\) and \(T_ x\), \(T_ y\) are diagonal matrices with diagonal entries \(\pm 1\). Another main result is dealt with the set of real eigenvalues of the matrices contained in some interval matrix \(A_ I\). Let this set be called \(L\). Then it is shown that any \(\lambda\in L\) is an eigenvalue of a matrix of type \(A_ s\). Further, each boundary point of \(L\) corresponds to some boundary matrix of \(A_ I\). Under certain assumptions regarding sign stability, \(L\) turns out to be the union of at most \(n\) compact intervals. Finally it is proven from various assumptions that an interval matrix is stable iff two sample matrices which are explicitly known are stable.