How can I design a Python function to print a matrix with only the forward diagonal elements set to True?

The problem is that the shorthand you're using to create lists actually just creates copies of the same list. You can check this with the id function:

n = 5
dp = [[False]*n]*n
print([id(x) for x in dp])

The reason is that multiplying with * does not create new object, as @TobyPetty mentioned.

The way to fix would be:

def func(n):
    dp = [[[False] for i in range(n)] for x in range(n)]
    for i in range(n):
        dp[i][i] = True
    print(dp)