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Question
Let A=⎡⎢⎣−123⎤⎥⎦ and B=[−2−1−4], then matrix (AB)A equals
Let A=⎡⎢⎣−123⎤⎥⎦ and B=[−2−1−4], then matrix (AB)A equals
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Solution
The correct option is C −12A
A=⎡⎢⎣−123⎤⎥⎦,B=[−2−1−4]
AB=⎡⎢⎣214−4−2−8−6−3−12⎤⎥⎦
(AB)A=⎡⎢⎣214−4−2−8−6−3−12⎤⎥⎦⎡⎢⎣−123⎤⎥⎦
⇒(AB)A=⎡⎢⎣12−24−36⎤⎥⎦=−12⎡⎢⎣−123⎤⎥⎦=−12A
A=⎡⎢⎣−123⎤⎥⎦,B=[−2−1−4]
AB=⎡⎢⎣214−4−2−8−6−3−12⎤⎥⎦
(AB)A=⎡⎢⎣214−4−2−8−6−3−12⎤⎥⎦⎡⎢⎣−123⎤⎥⎦
⇒(AB)A=⎡⎢⎣12−24−36⎤⎥⎦=−12⎡⎢⎣−123⎤⎥⎦=−12A
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