One of the proofs below, however, will have some similarity to this argument, by introducing a matrix with non-numeric coefficients in which A can really live inside an entry, but then A I_n is not equal to A, and the conclusion is reached differently.
One of the proofs below, however, will bear some similarity to this non-proof. By introducing a matrix with non-numeric coefficients, we can actually let A lives inside an entry, but then A I_n is not equal to A, and the conclusion is reached differently.