# Math Help - a question on invertible matrices

1. ## a question on invertible matrices

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

2. If B has an inverse, so does $B^T$. What is $(B^TA)(A^{-1}(B^T)^{-1})$ and $(A^{-1}(B^T)^{-1})(B^TA)$?