It is not possible. It can be explained, at least, in three ways:
1. It is equivalent to solve a system of three equations and nine unknowns.
2. The inverse matrix is only defined for a square matrix.
3. The matrix A that satisfies the equation is not unique: Any new matrix obtained by a linear combination of rows or columns satisfy also the equation.
Matrix product
It is not possible. It can be explained, at least, in three ways:
1. It is equivalent to solve a system of three equations and nine unknowns.
2. The inverse matrix is only defined for a square matrix.
3. The matrix A that satisfies the equation is not unique: Any new matrix obtained by a linear combination of rows or columns satisfy also the equation.
Regards
Re:
Agree with Faustino,
A simple example is:
A=[14,0,0;0,16,0;0,0,50/3] also satisfies the equation.
many answers
there are many A satisfying your request.