If $A$ and $B$ are two n×n nonsingular matricesm, prove that $B^TA^{-1}$ is nonsingular and $(B^TA^{-1})^{-1}=A(B^{-1})^T$
2. First, can you prove that if A is non-singular, the $A^T$ is non-singular and $(A^T)^{-1}= (A^{-1})^T$. (Use the definition of " $A^T$".