Heisenberg had not proceeded very far with this idea before he noticed that it would lead to his physical quantities not satisfying the commutative law of multiplication.

在意识到矩阵表示将导致物理量不满足乘法交换律之前，海森堡并没有前进太远。

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We then can verify the associative law and the commutative law for multiplication, and the uniqueness of the result of addition indicates the uniqueness and the cancellation law for multiplication.

我们容易验证乘法满足结合律和交换律，并且由加法结果的唯一性得出乘法结果的唯一性和乘法消去律。

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