Let's go over the question visible in your image.

The question is asking for the composite transformation $A$ followed by $B$, where:

• Matrix $A = \begin{pmatrix} 2 & 0 \\ -1 & 3 \end{pmatrix}$
• Matrix $B = \begin{pmatrix} 1 & 2 \\ -2 & -3 \end{pmatrix}$

To find the composite transformation, we need to calculate the product $B \times A$ (Matrix $A$ followed by $B$).

Let me compute that for you.

We are multiplying:

$B \times A = \begin{pmatrix} 1 & 2 \\ -2 & -3 \end{pmatrix} \times \begin{pmatrix} 2 & 0 \\ -1 & 3 \end{pmatrix}$

Now, I will compute the result.The composite transformation $B \times A$ is:

$\begin{pmatrix} 0 & 6 \\ -1 & -9 \end{pmatrix}$

Now, looking at the available answer options in the image, the correct option matches the matrix:

$\begin{pmatrix} 0 & 6 \\ -1 & -9 \end{pmatrix}$

Let me know if you'd like any further clarification or details!

Here are some related questions to deepen your understanding:

1. What is the process for multiplying two 2x2 matrices?
2. How does matrix multiplication apply to transformations in geometry?
3. Can you find the inverse of matrix $A$? How is it useful?
4. How does the order of matrix multiplication affect the result?
5. What are some real-life applications of matrix transformations?

Tip: When performing matrix multiplication, always ensure the number of columns in the first matrix matches the number of rows in the second matrix.