Simple matrix question about $\begin{bmatrix}a & b\\c & d\end{bmatrix}$ I have a question about this matrix:
$\begin{bmatrix}a & b\\c & d\end{bmatrix}$
Show that if  $D = ad − cb$ does not equal $0$, then $A^{-1}$ = $D^{-1}*\begin{bmatrix}d & -b\\-c & a\end{bmatrix}$
How do I show this?  Can someone help?

By definition, the inverse matrix $A^{-1}$ satisfies
$$
    A A^{-1} = A^{-1} A = I
$$
where $I$ is the (in this case, $2\times 2$) identity matrix.  To show the matrix $B = \frac{1}{D}\begin{bmatrix} d & -b \\ -c & a \end{bmatrix}$ is equal to $A^{-1}$, it suffices to show $AB = I$.  
