1
Question
If A=⎡⎢⎣−245⎤⎥⎦,B=[13−6], verify that (AB)′=B′A′.
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Solution
A=⎡⎢⎣−245⎤⎥⎦B=[13−6](AB)=B′A′LHS=(AB)′=⎛⎜
⎜
⎜
⎜⎝⎡⎢⎣−245⎤⎥⎦3×1[13−6]1×3⎞⎟
⎟
⎟
⎟⎠1=⎡⎢⎣−2−6+12412−24515−30⎤⎥⎦1=⎡⎢⎣−245−6121512−24−30⎤⎥⎦RHS=B′A′=⎡⎢⎣13−6⎤⎥⎦[−245] =⎡⎢⎣−245−6121512−24−30⎤⎥⎦.
LHS=(AB)′=⎛⎜
⎜
⎜
⎜⎝⎡⎢⎣−245⎤⎥⎦3×1[13−6]1×3⎞⎟
⎟
⎟
⎟⎠1
=⎡⎢⎣−2−6+12412−24515−30⎤⎥⎦1
=⎡⎢⎣−245−6121512−24−30⎤⎥⎦
RHS=B′A′=⎡⎢⎣13−6⎤⎥⎦[−245]
=⎡⎢⎣−245−6121512−24−30⎤⎥⎦.
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