Solution:

Given matrix A = [1 -2 1 0 1 -1 3 -1 1]

To find A3 - 3A2 - A - 3I, we need to perform the following operations:

1. Calculate A3:
A3 = A * A * A

2. Calculate A2:
A2 = A * A

3. Calculate -3A2:
-3A2 = -3 * A2

4. Calculate -A:
-A = -1 * A

5. Calculate -3I:
-3I = -3 * I

6. Add all the calculated matrices together:
A3 - 3A2 - A - 3I = A3 + (-3A2) + (-A) + (-3I)

Now, let's break down each step in detail:

Step 1: Calculate A3:
To calculate A3, we need to multiply matrix A with itself three times:

A3 = A * A * A

Multiplying A with itself gives us:

A2 = A * A = [1 -2 1] * [0 1 -1] = [2 -3 2]

Multiplying A2 with A gives us:

A3 = A2 * A = [2 -3 2] * [1 -1 3] = [-2 -1 5]

So, A3 = [-2 -1 5]

Step 2: Calculate A2:
We have already calculated A2 as [2 -3 2] in the previous step.

Step 3: Calculate -3A2:
To calculate -3A2, we need to multiply A2 with -3:

-3A2 = -3 * [2 -3 2] = [-6 9 -6]

Step 4: Calculate -A:
To calculate -A, we need to multiply matrix A with -1:

-A = -1 * [1 -2 1 0 1 -1 3 -1 1] = [-1 2 -1 0 -1 1 -3 1 -1]

Step 5: Calculate -3I:
To calculate -3I, we need to multiply the identity matrix I with -3:

-3I = -3 * [1 0 0 0 1 0 0 0 1] = [-3 0 0 0 -3 0 0 0 -3]

Step 6: Add all the calculated matrices together:
Now, we can add A3, -3A2, -A, and -3I together:

A3 - 3A2 - A - 3I = [-2 -1 5] + [-6 9 -6] + [-1 2 -1 0 -1 1 -3 1 -1] + [-3 0 0 0 -3 0 0 0 -3]

Simplifying this expression gives us the final result.

Note: The final result will be a matrix with the same dimensions as the original matrix A.