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Question
If A=[1−23−425] and B=⎡⎢⎣234521⎤⎥⎦. Find AB and show that AB≠BA
If A=[1−23−425] and B=⎡⎢⎣234521⎤⎥⎦. Find AB and show that AB≠BA
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Solution
The correct option is D AB=[0−4103]
Given, A=[1−23−425],B=⎡⎢⎣234521⎤⎥⎦AB=[1−23−425]⎡⎢⎣234521⎤⎥⎦=[2−8+63−10+3−8+8+10−12+10+5]=[0−4103]BA=⎡⎢⎣234521⎤⎥⎦[1−23−425]=∣∣
∣∣2−12−4+66+154−20−8+1012+252−4−4+2−6+5∣∣
∣∣⎡⎢⎣−10221−16237−2−2−1⎤⎥⎦Hence AB≠BA
Given,
A=[1−23−425],B=⎡⎢⎣234521⎤⎥⎦AB=[1−23−425]⎡⎢⎣234521⎤⎥⎦=[2−8+63−10+3−8+8+10−12+10+5]=[0−4103]BA=⎡⎢⎣234521⎤⎥⎦[1−23−425]=∣∣
∣∣2−12−4+66+154−20−8+1012+252−4−4+2−6+5∣∣
∣∣⎡⎢⎣−10221−16237−2−2−1⎤⎥⎦
Hence AB≠BA
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