If $A$ and $B$ are $n\times n$ matrices, then $((AB)^{-1})^T=(A^{-1})^T (B^{-1})^T$

Question

Please help me to solve this.

Prove that if $A$ and $B$ are $n\times n$ matrices, then $((AB)^{-1})^T=(A^{-1})^T (B^{-1})^T$.

a problem involve transpose and inverse of matrices. check the attachment
a product of two matrices ,the transpose of the inverse of AB

Answer 1

Do you understand the properties of inverse and transpose? remark $$(AB)^{-1}=B^{-1}A^{-1}$$ and $$(AB)^T = B^T A^T.$$