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Give an example of three matrices A ,...

Give an example of three matrices `A ,\ B ,\ C` such that `A B=A C` but `B!=C` .

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Let `A=[{:(1,0),(0,0):}]B=[{:(2,3),(4,0):}]"and" C=[{:(2,3),(4,4):}]`
` therefore AB=[{:(1,0),(0,0):}][{:(2,3),(4,0):}]=[{:(2,3),(0,0):}]`
and `AC=[{:(1,0),(0,0):}][{:(2,3),(4,4):}]=[{:(2,3),(0,0):}]`
Thus, we see that AB=AC
where, A is non-zero matrix but `BneC`.
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