Output of that code My Question is not about python code, but related to linear algebra or Matrix properties(like additive, distributive)

How to explain the following operation mathematically

X = X0 append/Concat X1  
(X.Transpose Multiply X) result same of (X0.Transpose Multiply X0) + (X1.Transpose Multiply X1)

here X1 is appended to X0 then and stored in X, then multiplied X with X transpose. the result is the same as (X0.T Multiply X0) + (X1.T Multiply X1) I gave the python code snippets of that to execute and see. So, I am trying to understand, how I can explain it with linear Algebra or Matrix multiplication properties.

import numpy as np
X0 = np.array([[1, 1, 1, -1, 1, -1, -1, 1, -1],
              ])
X1 = np.array([   [1, -1, 1, 1, -1, 1, 1, 1, 1],
                  ])
X = np.array([   [1, 1, 1, -1, 1, -1, -1, 1, -1],
    [1, -1, 1, 1, -1, 1, 1, 1, 1],
                  ])

W_t = (X.T @ X)


W0 = (X0.T @ X0) 
W1 = (X1.T @ X1) 

W = W0 + W1
print(W-W_t)