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The products commute, so the equation holds.  In essence, the matrix identity turns on the fact that the law of exponents <math>(a^b)^c = a^{bc}\!</math> in ordinary arithmetic holds when the values <math>a, b, c\!</math> are restricted to the boolean domain <math>\mathbb{B}.</math>  Regarded as a logical statement, the law of exponents <math>(a^b)^c = a^{bc}\!</math> amounts to a theorem of propositional calculus that is otherwise expressed in the following ways:

The products commute, so the equation holds.  In essence, the matrix identity turns on the fact that the law of exponents <math>(a^b)^c = a^{bc}\!</math> in ordinary arithmetic holds when the values <math>a, b, c\!</math> are restricted to the boolean domain <math>\mathbb{B} = \{ 0, 1 \}.</math>  Interpreted as a logical statement, the law of exponents <math>(a^b)^c = a^{bc}\!</math> amounts to a theorem of propositional calculus that is otherwise expressed in the following ways:

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