Can you use Mirror Force against Mirror Force in the card game Yu-Gi-Oh!?

My brother and I were playing Yu-Gi-Oh! He had a Summoned Skull with 5000 attack because of Mage Power, a Dark Magician in defense mode, and a face down card, in the spell and trap card zone he had 5 Spell/Trap cards including his Mage Power. On my side of the field I had Drillago, Wingweaver and the face down card Mirror Force. My brother attacked my Wingweaver with his Summoned Skull, and I used Mirror Force, then he used Mirror force. He told me all my monsters were wiped out. Is this possible? Or is he cheating me? Will all my monsters be wiped out?