Following the "single crossing point" property in the scalar Gaussian channel, we explored the matrix Q, which is the difference between the MMSE of a general Gaussian input and an arbitrary input. The result was somewhat surprising. A similar property of a "single crossing point" exists for every eigenvalue of the matrix Q. The usage of the "single crossing" point property on information theoretic problems provided interesting results and insightful proofs to problems such as: the trade-off between rate and the MMSE disturbance (and also disturbance measured by the mutual information), a converse proof to the Gaussian BC capacity region (both the scalar and the parallel vector cases), and recently the "information bottleneck" problem.