What is the proof for the similarity of two matrices having the same rank?

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SUMMARY

The discussion centers on the proof that two similar matrices possess the same rank. Similar matrices are defined as matrices A and B for which there exists an invertible matrix P such that B = P^(-1)AP. The rank of a matrix is the dimension of the vector space generated by its rows or columns. Therefore, since similarity transformations preserve linear combinations, the ranks of similar matrices are indeed equal.

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vdgreat
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can anyone help me with this proof

rank of two similar matrices is same.
 
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I would start by citing the definitions of "similar matrix" and "rank".
 

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