Problem #PRU-5137

Problem

Sixteen lightbulbs are arranged in a $4\times 4$ grid. Some of them are on, the other ones are off. You are allowed to change the state of all the bulbs in a column, in a row, or along any diagonal (note: there are $14$ diagonals in total!). Is it possible to go from the arrangement on the left to the one on the right by repeating this operation?