Question 1175738
You're on the right track with matrix multiplication! Let's break down how to calculate AB and BA step-by-step.

**Matrix Multiplication (AB)**

* **Dimensions:** First, check if the multiplication is possible. Matrix A is a 3x3 matrix, and matrix B is also a 3x3 matrix. Since the number of columns in A matches the number of rows in B, we can multiply them. The result will be a 3x3 matrix.

* **Calculation:**
    * To get the element in the first row and first column of AB, you multiply the first row of A by the first column of B:
        * (4 * 2) + (-4 * 2) + (-3 * -1) = 8 - 8 + 3 = 3 (You got this one right!)
    * To get the element in the first row and second column of AB, you multiply the first row of A by the second column of B:
        * (4 * 0) + (-4 * -2) + (-3 * -1) = 0 + 8 + 3 = 11
    * To get the element in the first row and third column of AB, you multiply the first row of A by the third column of B:
        * (4 * 2) + (-4 * 1) + (-3 * -2) = 8 - 4 + 6 = 10
    * To get the element in the second row and first column of AB, you multiply the second row of A by the first column of B:
        * (0 * 2) + (0 * 2) + (-2 * -1) = 0 + 0 + 2 = 2
    * To get the element in the second row and second column of AB, you multiply the second row of A by the second column of B:
        * (0 * 0) + (0 * -2) + (-2 * -1) = 0 + 0 + 2 = 2
    * To get the element in the second row and third column of AB, you multiply the second row of A by the third column of B:
        * (0 * 2) + (0 * 1) + (-2 * -2) = 0 + 0 + 4 = 4
    * To get the element in the third row and first column of AB, you multiply the third row of A by the first column of B:
        * (1 * 2) + (-4 * 2) + (-2 * -1) = 2 - 8 + 2 = -4
    * To get the element in the third row and second column of AB, you multiply the third row of A by the second column of B:
        * (1 * 0) + (-4 * -2) + (-2 * -1) = 0 + 8 + 2 = 10
    * To get the element in the third row and third column of AB, you multiply the third row of A by the third column of B:
        * (1 * 2) + (-4 * 1) + (-2 * -2) = 2 - 4 + 4 = 2

* **Result (AB):**
    ```
    AB = |  3  11  10 |
         |  2   2   4 |
         | -4  10   2 |
    ```

**Matrix Multiplication (BA)**

* **Dimensions:** Since both B and A are 3x3 matrices, BA is also possible, and the result will be a 3x3 matrix.
* **Calculation:**
    * To get the element in the first row and first column of BA, you multiply the first row of B by the first column of A:
        * (2 * 4) + (0 * 0) + (2 * 1) = 8 + 0 + 2 = 10
    * To get the element in the first row and second column of BA, you multiply the first row of B by the second column of A:
        * (2 * -4) + (0 * 0) + (2 * -4) = -8 + 0 - 8 = -16
    * To get the element in the first row and third column of BA, you multiply the first row of B by the third column of A:
        * (2 * -3) + (0 * -2) + (2 * -2) = -6 + 0 - 4 = -10
    * To get the element in the second row and first column of BA, you multiply the second row of B by the first column of A:
        * (2 * 4) + (-2 * 0) + (1 * 1) = 8 + 0 + 1 = 9
    * To get the element in the second row and second column of BA, you multiply the second row of B by the second column of A:
        * (2 * -4) + (-2 * 0) + (1 * -4) = -8 + 0 - 4 = -12
    * To get the element in the second row and third column of BA, you multiply the second row of B by the third column of A:
        * (2 * -3) + (-2 * -2) + (1 * -2) = -6 + 4 - 2 = -4
    * To get the element in the third row and first column of BA, you multiply the third row of B by the first column of A:
        * (-1 * 4) + (-1 * 0) + (-2 * 1) = -4 + 0 - 2 = -6
    * To get the element in the third row and second column of BA, you multiply the third row of B by the second column of A:
        * (-1 * -4) + (-1 * 0) + (-2 * -4) = 4 + 0 + 8 = 12
    * To get the element in the third row and third column of BA, you multiply the third row of B by the third column of A:
        * (-1 * -3) + (-1 * -2) + (-2 * -2) = 3 + 2 + 4 = 9

* **Result (BA):**
    ```
    BA = |  10 -16 -10 |
         |   9 -12  -4 |
         |  -6  12   9 |
    ```