Let A and B be two 2x2 matrices. Consider the statements(i)  AB=O⇒A=O or B=O(ii)  AB=I2⇒A=B−1(iii) (A+B)2=A2+2AB+B2Then

(i) is false. If A=0    10    −1 and B=1    10    0, thenAB=0    00    0=OThus, AB=O⇒A=O or B=O(iii) is false since matrix multiplication is not commutative.(ii) is true as product AB is an identity matrix, if and only if B is inverse of the matrix A.