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The invertible matrix theorem states that the columns of the given matrix form a linearly independent set. Can we argue that the rows of the same matrix also forms a linearly independent set? If a matrix is invertible, then inverse of a given matrix [tex]A^{-1}[/tex] has it's columns being linearly independent (for [tex]A^{-1}[/tex]) which is equivalent to the rows of A being linearly independent. So can we say that both the rows and columns of A form a linearly independent set?
Thanks,
JL
Thanks,
JL