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).
You should be able to use expansion by minors in an inductive proof.