Are these matrix statements true or false?

1) If A and B are both invertible then AB - BA is not invertible.





2) If ABC = I then B is invertible.





I am sooo lost...any insight would be AWEsome!Are these matrix statements true or false?
1) False





A =


1....1


0....1





B =


1....0


1....1





Then AB - BA =


1....0


0...-1





2) True





Each of A, B, and C must have non-zero determinant if their product is I, which has determinant 1.