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If A and B are square matrices of same o...

If A and B are square matrices of same order such that `AB=O` and `B ne O`, then prove that `|A|=0`.

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We have `AB=O`
`:. |AB|=0`
`implies |A||B|=0`
`implies |A|=0` or `|B|=0`
Now, let `|A| ne 0`, then `A^(-1)` exists.
Thus, from `AB=O`,
`A^(-1) AB=A^(-1)O`
`:. IB=O`
or `B=O`
But it is given that `B ne O`, then `|A|=0`.
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