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## Main Question or Discussion Point

Hello,

Would it be correct to say that if for every two

Would it be correct to say that if for every two

__different__vectors x and y, A*x ≠ A*y (where A is a symmetrical matrix), then A is NOT necessarily invertible? In other words, albeit for any two different vectors x and y symmetrical matrix A times one of the vectors is not equal to A times the other, A is not necessarily invertible?