As#9: Polarization of Light and Malus's Law (PART F)

The question reads:

Notice that a polarizer modifies the light intensity according to Malus's law and also reorients the polarization angle of the beam to match its own transmission axis. Hence it is possible for light to pass through a pair of crossed polarizers if a third polarizer is inserted between them with an intermediate transmission axis direction. What is the new intensity of the light emerging from the final polarizer in Part E if a third polarizer (Polarizer A in the figure (Part F figure) ), whose transmission axis is offset 45 from each of the others, is inserted between the original two polarizers?

I thought that becuase the first polarizer and the third polarizer are perpendicular to each other, they would form an intensity of zero regardless of whatever angle the second polarizer is positioned at in the misddle. I dont understand this.

Any help?