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I believe it is not possible to be performed with non-square matrices
what do you mean by "4*4 byte binary matrix"?
a 4 x 4 matrix of integers in [-128, 127] where "+" is "+ mod 256" and "*" is "* mod 256"? This might not have an inverse.
a 4 x 4 matrix of integers in [0, 255] where "+" is "+ mod 256" and "*" is "* mod 256"? This might not have an inverse.
This is because some elements do not have inverses themselves. for example 1 = (2 * x) mod 256 has no solution if x must be an integer.
a 32 x 32 matrix of {0,1} where "+" is "xor" and "*" is "and"? This could have an inverse.
a 4 x 4 matrix of elements of a gf256? This could have an inverse.
These don't have numeric interpretations.
What part are you having trouble with? You may be having problems as 8b values can have 256 values, but 256 is not a prime number. As a result, not all bytes have a modular inverse.
I need a general algorithm to apply it on any matrix like that in the previous image regardless its value ..