suppose A and B are invertible matrices.

Show that Bt is also invertible by producing a matrix C such that (BtA)C=I and C(BtA)=I

thanks

Mr F edit:The OP adds that t is the transpose. So the question is probably the following:

Suppose A and B are invertible matrices.

Show that $\displaystyle B^T$ is also invertible by producing a matrix C such that $\displaystyle (B^T A) C = I$ and $\displaystyle C (B^T A) = I$.