Originally Posted by

**Ackbeet** So far as I know, the definition of a matrix inverse that is typically used is the one I gave in Post # 6. The inverse of 5 is that number such that, when you multiply it by 5, you get 1. So that'd be 1/5, because 5(1/5)=(1/5)5=1. Similarly, the inverse of

$\displaystyle \begin{bmatrix}2 &0\\ 0 &3\end{bmatrix}$

is

$\displaystyle \begin{bmatrix}1/2 &0\\ 0 &1/3\end{bmatrix},$

because

$\displaystyle \begin{bmatrix}2 &0\\ 0 &3\end{bmatrix}\begin{bmatrix}1/2 &0\\ 0 &1/3\end{bmatrix}=\begin{bmatrix}1/2 &0\\ 0 &1/3\end{bmatrix}\begin{bmatrix}2 &0\\ 0 &3\end{bmatrix}=\begin{bmatrix}1 &0\\ 0 &1\end{bmatrix}=I.$

I'm not sure I understand your definition of the matrix inverse. What does the asterisk mean in your definition?