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...)

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- Jan 23rd 2013, 08:19 AMguybrush92Matrix Proof
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...) - Jan 23rd 2013, 08:40 AMBobPRe: Matrix Proof
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. - Jan 23rd 2013, 09:54 AMDevenoRe: Matrix Proof
by definition an inverse for an nxn matrix A is an nxn matrix B such that AB = I.

and....

$\displaystyle A^T(A^{-1})^T = (A^{-1}A)^T = I^T = I$