# Solving a matrix equation with overdetermined case

I have a matrix equation $$\begin{bmatrix} a& e& i\\ b & f & j\\ c & g &k\\ d & h& l\end{bmatrix}.B=\begin{bmatrix} d& c&i\\ g&e&f\\ a&f&h\\ b&k&l\end{bmatrix}$$, Here $$B$$ is $$3\times 3$$ matrix. This becomes an overdetermined systems. Is there any solution, and if not what conditions can be imposed on the matrix entries for the solution to exist.

• Is $B$ a known, matrix with numerical entries ? – Jean Marie Jan 7 at 18:34
• Have a look at pseudo inverse – Damien Jan 7 at 19:15
• $B$ is the transformation matrix that i need to calculate,it is unknown – Upstart Jan 7 at 19:29