What is the projection matrix of A onto its row space, if A is $\mathbb{R^{m*n}}$ with linearly independent rows

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I know that the projection matrix of A onto its column space, if A is $\mathbb{R^{m*n}}$ with linearly independent columns is $P=A(A^TA)^{-1}A^Tb$ Does this follow for the projection matrix of A onto its row space, if A is $\mathbb{R^{m*n}}$ with linearly independent rows