When applicable…

(i) combining by addition a quantity with its additive inverse (opposite) yields the additive identity (0).

(ii) combining by multiplication a quantity with its multiplicative inverse (reciprocal) yields the multiplicative identity (1).

(iii) combining by composition a function with its (functional) inverse yields the identity function f(x)=Id(x)=x.

This continues outside of high school algebra because

(iv) combining by matrix multiplication a matrix with its inverse (matrix) yields the identity matrix

and so on… ]]>

This comes up everywhere:

– 3+4 is equivalent to 7

– the equation 2x + 1 = 6 is equivalent to 2x = 5

– we rationalize denominators be multiplying be a special form of 1

– we solve polynomial equations by creating equivalent factored forms

– we use identities in trigonometry to simplify expressions and solve equations

And the list goes on.

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