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