For this question, how do you get BA(BA - I) = 0?

Suppose A, B are n x n matrices and that AB = I. Show that then BA = I. Hint: First explain why det(A), det(B) are both nonzero. Then (AB) A = A and then show BA( BA - I) = 0. From this use what is given to conclude A(BA - I) = 0. Then use Exercise 3. E. 36