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

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(i) is false, (ii) and (iii) are true

(i) and (iii) are false, (ii) is true

(i) and (ii) are false, (iii) is true

(ii) and (iii) are false, (i) is true

answer is B.

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Detailed Solution

(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.

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