# Homework Help: Showing a matrix is invertible

1. Feb 19, 2014

### noelo2014

1. The problem statement, all variables and given/known data

let A and B be nXn invertible matrices. Show that (A.B)T is invertible by finding it's inverse

2. Relevant equations

3. The attempt at a solution

(A.B)T=BT.AT

Last edited: Feb 19, 2014
2. Feb 19, 2014

### CAF123

You are looking for a matrix $C$ such that $(AB)^{T}C = C(AB)^T = I_{n}$. The question does not say that A and B are invertible, however given that the inverse of (AB)T exists you can show that they are indeed invertible.

3. Feb 19, 2014

### noelo2014

Sorry I left out the fact that A and B are invertible.

4. Feb 19, 2014

### HallsofIvy

You have already said that $(AB)^T= B^TA^T$. Okay, what will get rid of that $B^T$ and then what will get rid of that $A^T$

(Of course, you know that a matrix is invertible if and only if its determinant is not 0? And that the determinant of $X^T$ is the same as the determinant of $X$?)