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If (AB)'=B′A′ , where A and B are not square matrices, then the number of rows in A is equal to the number of columns in B and the number of columns in A is equal to the number of rows in B .

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    Payal Gupta | Contributor-Level 10

    2 months ago

    This is a True or False Type Questions as classified in NCERT Exemplar

    T r u e . L e t     A = [ a i j ] m × n     a n d     B = [ b i j ] p × q A B     i s     d e f i n e d     w h e n     n = P ∴                                 O r d e r     o f     A B = m × q ⇒                               O r d e r     o f     ( A B ) ' = q × m O r d e r     o f     B ' i s     q × p     a n d     o r d e r     o f     A ' i s     n × m ∴ B ' A '     i s     d e f i n e d     w h e n     P = n a n d     t h e     o r d e r     o f     B ' A '     i s     q × m H e n c e ,     O r d e r     o f     ( A B ) ' = O r d e r     o f     B ' A '     i . e . ,     q × m .

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