# Thread: Show that if M is invertible, M^t is also invertible

1. ## Show that if M is invertible, M^t is also invertible

hmm, how do i prove this one?

plus,

(M^t)^-1 = (M^-1)^t

2. Originally Posted by experiment00
hmm, how do i prove this one?

plus,

(M^t)^-1 = (M^-1)^t

from
$A^T(A^{-1})^T=(A^{-1}A)^T=I^T = I$
we conclude that it's really
$(A^{-1})^T=(A^T)^{-1}$

3. if M is invertible, then $\det(M)\neq 0$

$\because~\det(M^T)=\det(M)\neq 0$, so $M^T$ is invertible