Matrix associativity in tensorflow tf.matmul issues - numpy

Question

We have a matrix M with shape (n, n) and a matrix C with shape (n, n). In this example, both matrices are generate using numpy's np.random.normal(). We are encountering some unexpected behaviour in the associativity property of matrix multiplication in both numpy and tensorflow. This is causing my model (written in tensorflow) to give some unexpected errors when computing the Cholesky decomposition of covariance matrices.
Below is a simple working example of this (the model actually uses 3D and 4D tensors):
import numpy as np
import tensorflow as tf
# Generate random matrices sampled from normal distribution
M = np.random.normal(0, 0.1, size=(5, 5))
C = np.random.normal(0, 0.1, size=(5, 5))
First we check numpy output:
r1 = np.matmul(np.matmul(M, C),np.transpose(M))
r2 = np.matmul(M, np.matmul(C, np.transpose(M)))
r3 = (M # C) # np.transpose(M)
r4 = M # (C # np.transpose(M))
print("r1 == r2: ", np.all(r1 == r2))
print("r1 == r3: ", np.all(r1 == r3))
print("r1 == r4: ", np.all(r1 == r4))
print("r2 == r3: ", np.all(r2 == r3))
print("r2 == r4: ", np.all(r2 == r4))
print("r3 == r4: ", np.all(r3 == r4))
We get the following result:
Numpy's result.
The we check tensorflow output:
# Check tensorflow
t1 = tf.linalg.matmul(tf.linalg.matmul(M, C), M, transpose_b = True)
t2 = tf.linalg.matmul(M, tf.linalg.matmul(C, M, transpose_b = True))
print("t1 == t2: ", np.all(t1.numpy() == t2.numpy()))
print(t1.numpy() - t2.numpy())
We get the following result:
Tensorflow's results.
I found a similar thread describing a similar issue here, but with no answer.
Do you think that differences in the order of approximately e-19 can have such an impact that causes these weight matrices to not have a Cholesky decomposition?
Thanks in advance.