Hello Natasha
Although admit is necessary, you must always carry your id proof. Not just because it may be required in the exam, it may be useful to you for reasons you can't even think of. You are going to have one of the important exam, so why take a chance. Having an I'd proof may not trouble you as much as being without I'd card can. Afterall it's the question of your hard work and struggling preparations. So it would be absolutely alright to carry it anyway. All the best for your exam