Is it a stochastic matrix?

Haskell, 57 55 bytes

import Data.List
s a=all((==100).sum)<$>[transpose a,a]

Input of type (Eq a, Num a) => [[a]]. Outputs boolean list [left-stochastic, right-stochastic]

Thanks to @proudhaskeller for saving 2 bytes

R, 55 bytes

function(m)c(all(colSums(m)==100),all(rowSums(m)==100))

Unnamed function where m is assumed to be an R-matrix.

Output:

• [1] TRUE FALSE: Left stochastic
• [1] FALSE TRUE: Right stochastic
• [1] TRUE TRUE: Doubly
• [1] FALSE FALSE: None

05AB1E, 13 11 10 bytes

Right stochastic: [0,1]
Left stochastic: [1,0]
Doubly stochastic: [1,1]
None of those: [0,0]

Dø2FOTnQPˆ

Try it online!

Explanation

D            # duplicate input
 ø           # transpose the copy
  2F         # 2 times do (once for each matrix)
    O        # sum of the rows
     TnQ     # is equal to 100
        P    # product
         ˆ   # add to global list
             # implicitly print global list at the end of the program