1
Question
If A=⎡⎢⎣−245⎤⎥⎦ and B=[13−6] verify that (AB)′=B′A′.
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Solution
Given : A=⎡⎢⎣−245⎤⎥⎦ and B=[13−6]⟹A′=[−245] and B′=⎡⎢⎣13−6⎤⎥⎦
Consider B′A′=⎡⎢⎣13−6⎤⎥⎦[−245]=⎡⎢⎣−245−6121512−24−30⎤⎥⎦Consider AB=⎡⎢⎣−245⎤⎥⎦[13−6] =⎡⎢⎣−2−612412−24515−30⎤⎥⎦
⟹(AB)′=⎡⎢⎣−245−6121512−24−30⎤⎥⎦=B′A′Hence, (AB)′=B′A′
⟹A′=[−245] and B′=⎡⎢⎣13−6⎤⎥⎦
Consider B′A′=⎡⎢⎣13−6⎤⎥⎦[−245]=⎡⎢⎣−245−6121512−24−30⎤⎥⎦
Consider AB=⎡⎢⎣−245⎤⎥⎦[13−6]
=⎡⎢⎣−2−612412−24515−30⎤⎥⎦
⟹(AB)′=⎡⎢⎣−245−6121512−24−30⎤⎥⎦=B′A′
Hence, (AB)′=B′A′
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