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Byju's Answer
Standard XII
Mathematics
Multiplication of Matrices
If A = [ 1 ...
Question

If A=⎡⎢⎣11−12−343−23⎤⎥⎦, B=⎡⎢⎣−1−2−161265105⎤⎥⎦ and C=⎡⎢⎣−1−1122−2−3−33⎤⎥⎦,
which if the following are null matrices ?

A
CA
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B
AB
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C
BA
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D
AC
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Solution

The correct options are
A CA
B AB
Given A=⎡⎢⎣11−12−343−23⎤⎥⎦, B=⎡⎢⎣−1−2−161265105⎤⎥⎦ and C=⎡⎢⎣−1−1122−2−3−33⎤⎥⎦

CA=⎡⎢⎣−1−1122−2−3−33⎤⎥⎦⎡⎢⎣11−12−343−23⎤⎥⎦=⎡⎢⎣000000000⎤⎥⎦=O

AB=⎡⎢⎣11−12−343−23⎤⎥⎦⎡⎢⎣−1−2−161265105⎤⎥⎦=⎡⎢⎣000000000⎤⎥⎦=O

BA=⎡⎢⎣−1−2−161265105⎤⎥⎦⎡⎢⎣11−12−343−23⎤⎥⎦=⎡⎢⎣−87−1048−426040−3550⎤⎥⎦≠O

AC=⎡⎢⎣11−12−343−23⎤⎥⎦⎡⎢⎣−1−1122−2−3−33⎤⎥⎦=⎡⎢⎣44−4−20−2020−16−1616⎤⎥⎦≠O

Hence, options A and B.

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