Checker shadow illusion

The checker shadow illusion is an optical illusion published by Edward H. Adelson, Professor of Vision Science at MIT in 1995.
Description.
The image depicts a checkerboard with light and dark squares, partly shadowed by another object. The optical illusion is that the area labeled A appears to be a darker color than the area labeled B. However, within the context of the two-dimensional image, they are of identical brightness, i.e., they would be printed with identical mixtures of ink, or displayed on a screen with pixels of identical colour. 
Verification.
That the two squares are the same color can be proven using any of the following methods: