OK serious questions:

Can you post the code you have sofar?

What did you expect?

What did you get?

What have you tried sofar?

What is the size of the square matrices? 5x5 4x4 3x3 2x2 1x1 ?

What Arduino are you using as there are square matrices that won't fit in an UNO, you might need a MEGA for them.

Should the code include matrix X vector?

Should the code include multiplication of different size square matrices?

Should the matrix multiplication algorithm include specific optimizations or algorithms like Gauss-Jordan elimination with partial pivoting?

The members of the matrices, are these char, byte, int, long, float ? (un)signed?

Should the code include error handling?

- in the serial communication part (non digit input, missing bytes, checksum errors etc)

- In the math part (overflow, underflow, divide by zero)

What are allowed baudrates for your application?

Are you familiar with the playground and tutorial sections of the Arduino where many example code snippets live?

Can you give an example of typical matrices?

In short, can you explain more about the assignment as it is not unambiguous to me yet