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Question

Consider the laws of exponents $A^{\prime} A^{\prime}=A^{r+1}$ and $\left(A^r\right)^{\prime \prime}=A^{r s}$. Show that if $A$ is invertible, then these laws hold for all negative integer values of $r$ and $s$.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3If r and s are negative integers,

then let $\mathrm{p}=-\mathrm{r}$ and $\mathrm{q}=-\mathrm{s}$ ( p and q are positive)

By definition, if A is invertible, $A^{-n}=(A^{-1})^{n}.

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