Python 3; tried going for a more efficient solution (I'm not sure how good it is compared to /u/-P-e-t-e-r- 's solution. Also, I started using Python yesterday, so any improvements would be great.

def isLatinSquare(dict_pos):
    for ipos in dict_pos.keys():
        pos = dict_pos[ipos]
        for icount in pos[0].keys():
            count = pos[0][icount]
            if count > 1:
                return False
        for icount in pos[1].keys():
            count = pos[0][icount]
            if count > 1:
                return False
    return True

#get input
print("Enter the length of the array.")
n = int(input())
print("Enter the array.")
array_inputted = input().split()

#store positions
dict_pos = {}
for i in range(n*n):
    num = array_inputted[i]
    x, y = divmod(i, n)
    if num in dict_pos:
        dict_pos[num][0][y] = dict_pos[num][0].get(y, 0) + 1
        dict_pos[num][1][x] = dict_pos[num][1].get(x, 0) + 1
    else:
        dict_pos[num] = [{y:1}, {x:1}]
    #print(f"dp[{num}][x][{y}]={dict_pos[num][0][y]}; dp[{num}][y][{x}]={dict_pos[num][1][x]}")

#evaluate
result = isLatinSquare(dict_pos)
print(result)