>>332120
If we take multiplication for ◦, an annihilator value would be 0: 1*0 = 2*0, but 1 != 2. And with complex number arithmetic, even different g1/g2 when multiplied by same value f can result in equal values. Latter is best demonstrated by matrix representation and defining product as matrix multiplication: [[1, 1]] * [[1], [2]] = [[1, 1]] * [[2], [1]], but [[1], [2]] != [[2], [1]].