Rank of a Matrix $C = A'B'$

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How to find a rank of a $3\times2$ matrix ?

$A$ is a $3\times3$ matrix . $B$ is a$2\times3$ matrix. I wrote $A'B'$ as $(BA)'$ . Did the multiplication and took the transpose and got a $3\times2$ matrix . Now how do I find the rank of $C$ which is a $3\times2$ matrix? Please help

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Your final matrix C is a non square matrix with more rows than columns.

The rank of a non-square matrix with dimensions $mXn$ cannot be more than the least of the dimensions i.e $rank(C)\leq min(m,n)$.

So, what one can say is that the rank of C cannot be more than 2. If you want to be sure, you need to check whether the columns are linearly independant or not. If they aren't, then the rank is 1.