$A$ is an invertible $n \times n$ matrix. Interpret each row of $A$ as a point in $\mathbb{R}^n$; then these $n$ points define a unique hyperplane in $\mathbb{R}^n$ that passes through each point (this hyperplane does not intersect the origin). Under this geometric interpretation, $A^{-1}$ has ...

The tags matrix-analysis (32 questions tagged) and matrix-theory (18 questions) should probably be merged, unless there is a strong difference between them that I am not aware of (incidentally, there is also matrices, 150 questions tagged). The tag matrix-inverse (6 questions) seems overly speci...