strassen based matrix inverse

i am trying to write a program to get the inverse of any type of square matrix using strassen based matrix inversion.
but what i don't understand is how to represent the sub-block matrix in the form A^-1, B^-1 etc...

since i have to apply it to different matrixes i can't really use something like
A^-1 = 1/determinant. so how to implement the blockkwise inverse.
a code would really be helpful.
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