# Why must the transpose of an invertible matrix be invertible?

##### 1 Answer

Nov 7, 2015

If

#### Explanation:

If you are happy to accept that

Suppose

Then:

#(A^(-1))^T A^T = (A A^(-1))^T = I^T = I#

#A^T (A^(-1))^T = (A^(-1) A)^T = I^T = I#

So