Chapter 8.4, Problem 49PE

To determine

To prove: If $A=\left[\begin{array}{ccc}a& 0& 0\\ 0& b& 0\\ 0& 0& c\end{array}\right],a\ne 0,b\ne 0,c\ne 0$ then $A^{-1}=\left[\begin{array}{ccc}\frac{1}{a}& 0& 0\\ 0& \frac{1}{b}& 0\\ 0& 0& \frac{1}{c}\end{array}\right]$.