Let P and Q be two 2×2matrices. Consider the statements i) PQ=O⇒P=Oor Q=O or bothii) PQ=I2⇒P=Q−1iii) (P+Q)2=P2+2PQ+Q2

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

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

All are false

All are true

answer is B.

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Detailed Solution

(i)PQ=0⇒P,Qneed not be zero matrix (ii)PQ=I2⇒P=Q−1is true(iii)(P+Q)2=P2+PQ+QP+Q2

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