In my syllabus we have the alternative definition of the condition of a matrix:

$\kappa (A)=\frac{{\text{max}}_{\Vert \overrightarrow{y}\Vert =1}\Vert A\overrightarrow{y}\Vert}{{\text{min}}_{\Vert \overrightarrow{y}\Vert =1}\Vert A\overrightarrow{y}\Vert}$

In it, it also says that by definition of the condition of a matrix it follows that $\kappa ({A}^{-1})=\kappa (A)$. So there is no explanation for this. Therefore, my question is: Why is $\kappa ({A}^{-1})=\kappa (A)$

$\kappa (A)=\frac{{\text{max}}_{\Vert \overrightarrow{y}\Vert =1}\Vert A\overrightarrow{y}\Vert}{{\text{min}}_{\Vert \overrightarrow{y}\Vert =1}\Vert A\overrightarrow{y}\Vert}$

In it, it also says that by definition of the condition of a matrix it follows that $\kappa ({A}^{-1})=\kappa (A)$. So there is no explanation for this. Therefore, my question is: Why is $\kappa ({A}^{-1})=\kappa (A)$