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  4. If A and B are non-zero square matrices of the same order such that AB = 0, then:

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Q. If A and B are non-zero square matrices of the same order such that AB = 0, then:

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Solution:

If A and B are non-zero square matrices of the same order such that
$AB = 0 \, \Rightarrow \, | AB | = 0$
$ \Rightarrow \, |A | | B | = 0$
$ \Rightarrow | A | = 0 $ or $| B | = 0$