Question: How to solve a Matrix Equation in Maple

I am attempting to use Maple to solve a matrix equation of the form aB^2+bB+cI=B^(−2), where B is a 3×3 matrix whose entries are constants which have been specified, and I is the 3×3 identity matrix (i.e. to find the values a, b and c which satisfy the equation).

My idea was to use a piece of code like


for matrix inversion to solve a system of three linear equations but that would assume that the right-hand side of the equation is a column vector when it is actually another 3×33×3 matrix. One other approach I took was to equate the left and right hand sides so that you add the three matrices on the LHS and then equate the resulting each entry with the corresponding entry of the matrix on the right hand side, however this gives me a set of 9 linear equations for 3 unknowns.  When I try to solve these with fsolve it says that there are more equations than there are unknowns. 

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