In this lab, you'll be practicing some interesting properties of a Dot Product-type matrix multiplication. Understanding these properties will become useful as you move forward with machine learning. The lab will require you to calculate results to provide a proof for these properties.

You will be able to:

• Understand and analytically explain Distributive, Commutative and Associative properties of dot product

• For each property, create suitably sized matrices with random data and prove the equations
• Ensure that size/dimension assumptions are met while performing calculations (you'll see errors otherwise)
• Calculate the LHS and RHS for all equations and show if they are equal or not

# Your code here

# Your code here 

# Your code here 

Note: superscipt^T denotes the transpose we saw earlier

# Your code here 

# Your code here 

You've seen enough matrix algebra by now to solve a problem of linear equations as you saw earlier. You'll now see how to do this next.