Originally Posted by

**adkinsjr** Do you know the definitions of transpose and inverse matrices? These are just simple operations, for the transpose you just interchange rows and columns.

If $\displaystyle A=\left[\begin{array}{ c c }a & b \\c & d \end{array} \right]$ then you can find the inverse using the formula:

$\displaystyle A^{-1}=\frac{1}{detA}\left[\begin{array}{ c c }d &- b \\-c & a \end{array} \right]$

where,

$\displaystyle det(A)=ad-bc$

So once you use that *plug-and-go* formula you just multiply the two matrices...$\displaystyle AA^{-1}$ if you multiply in opposite order $\displaystyle A^{-1}A$ it will be the same, which will be $\displaystyle I= \left[\begin{array}{ c c }1& 0 \\0 & 1 \end{array} \right]$ which is what they're asking you to demonstrate.