1
Question
If A=⎡⎢⎣11−12−343−23⎤⎥⎦ and B=⎡⎢⎣−1−2−161265105⎤⎥⎦, then which of the following is/are correct?
1. A and B commute.
2. AB is null matrix.
Select the correct answer using the code given below :
If A=⎡⎢⎣11−12−343−23⎤⎥⎦ and B=⎡⎢⎣−1−2−161265105⎤⎥⎦, then which of the following is/are correct?
1. A and B commute.
2. AB is null matrix.
Select the correct answer using the code given below :
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Solution
The correct option is B 2 only
We have, A=⎡⎢⎣11−12−343−23⎤⎥⎦ and B=⎡⎢⎣−1−2−161265105⎤⎥⎦AB=⎡⎢⎣−1+6−5−2+12−10−1+6−5−2−18+20−4−36+40−2−18+20−3−12+15−6−24+30−3−12+15⎤⎥⎦=⎡⎢⎣000000000⎤⎥⎦Hence, AB is a null matrix.and AB≠BAHence, B is the correct option.
We have, A=⎡⎢⎣11−12−343−23⎤⎥⎦ and B=⎡⎢⎣−1−2−161265105⎤⎥⎦
AB=⎡⎢⎣−1+6−5−2+12−10−1+6−5−2−18+20−4−36+40−2−18+20−3−12+15−6−24+30−3−12+15⎤⎥⎦
=⎡⎢⎣000000000⎤⎥⎦
Hence, AB is a null matrix.
and AB≠BA
Hence, B is the correct option.
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