Answer
See answer below
Work Step by Step
According to the Rank-Nullity Theorem, we have:
$dim (colspace (A))+dim (nullspace(A))=n$
Since $dim(colspace(A))=dim(nullspace(A))=d$
for every matrices $A$ in range $m \times n$
we have, $dim(colspace(A))+dim(nullspace(A))=2dim=n$
Hence, matrix $A$ has an even number of columns.
