Estimate original matrix from matrix multiplication result

Question

Let $A$ be $m \times n$ real matrix. Let $B$ be $n \times k$ real matrix. Let $C= A \times B$ ($m \times k$ matrix). Now, the question is: given $C$ and $A$, give an estimate for $B$. Possible estimate is $B_{\text{estimate}} = A^T × C$. Is there a way to interept this as best estimate? (Assuming ($A^TA$) not necessarily invertible). ($B$ can be thought as image representation).