Prove that $\det A$ does not exceed $1$ 
Let $A =(a_{ij}) ∈  M_n(\Bbb R)$ be a matrix with nonnegative entries such that the sum of the entries in each row does not exceed $1$. Prove that $|\det A|$ does not exceed $1$ too. 

This is one of my exercise,I tried to induction,but i'm stuck. 
Help me please! Thanks

You don't need induction. Prove/use the following two results: 1) the determinant is the product of the eigenvalues, and 2) any eigenvalue of a nonnegative matrix has magnitude at most the largest row sum (just write out the eigenvalue equation to see why).
