Monomial matrices (Generalized Permutation matrices ) We define Monomial matrices as following 
A matrix is said to be monomial if each row and column has 
exactly one non-zero entry. Let $N$ denote the set of monomial matrices
I want to show that it is a subgroup of $GL_{n}(F)$.
I have problem in showing that if $A\in N$ then its inverse also belongs to $N$.

Hint: The following are equivalent:


*

*$A \in N$ 

*$A = DP$ for some (invertible) diagonal matrix $D$ and permutation matrix $P$

*$A = PD$ for some (invertible) diagonal matrix $D$ and permutation matrix $P$

