I have a group of data as in the following figure:

$$A=\left[\begin{array}{ccc} [0.9\,\,0.6\,\,0.9\,\,0.2] & [0.4\,\,0.3\,\,0.1\,\,0.1] & [0.1\,\,0.3\,\,0.5\,\,0.6] \\ [0.6\,\,0.7\,\,0.2\,\,0.7] & [0.7\,\,0.8\,\,0.1\,\,0.6] & [0.8\,\,0.7\,\,0.8\,\,0.3] \\ [0.1\,\,0.6\,\,0.5\,\,0.3 & [0.8\,\,0.5\,\,0.4\,\,0.4] & [0.3\,\,0.6\,\,0.8\,\,0.5] \end{array}\right].$$

It is a 3x3 matrix whose elements are arrays. I even don't know how I can call it, but I need to know if the inverse of matrix $A$ ($A^{-1}$) is possible or not. Or is it mathematically correct approach to the inversion concept?

Thank you

Image of data set


the elements of your matrix are elements of $R^n$ for n=4.As far as i know there is not a way to define multiplication and prove that $R^4$ is a field .the definition of an inverse matrix is $AA^{-1}=I$ that requires multiplication of the elements of your matrix and its inverses. so i dont think you can do much about it.


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