Here it is given that A & B are inverse of each other.

∴ A^-1 = B -(i)

Also B^-1 = A -(ii)

From definition of inverse matrix, we know that-

→ AA^-1 = I

∵ A^-1 = B {from eq(i)}

→ AB = I -(iii)

Similarly, BB^-1 = I

∵ B^-1 = A {from eq(ii)}

→ BA = I -(iv)

So AB = BA = I {from eq(iii) and eq(iv)}

Hence option D is the correct answer.