Hey, I've been trying to prove that the inverse of the transpose of a matrix, is equal to the transpose of the inverse of a matrix, i.e.
$\displaystyle (A^T)^(-1)=(A^(-1))^T$
(also, some help on how to use TEX would be useful...)
Are you allowed to assume that $\displaystyle (AB)^{T}=B^{T}A^{T}$ ?
If so, take the transpose of $\displaystyle AA^{-1}=I$ and postmultiply by $\displaystyle (A^{T})^{-1}.$
For the LaTex input, use the Go Advanced option and 'press' the $\displaystyle \Sigma$ button and between the two [Tex] brackets type the line in as
(A^{T})^{(-1)}=(A^{(-1)})^{T}.
The ^ symbol translates as 'to the power of', and the power is then closed within the curley brackets.