The expression \((A \times B) \times (C \times D)\) involves matrix multiplication, which is associative. This means that the order in which the matrices are multiplied does not affect the result. We can group the matrices as:

\[
(A \times B) \times (C \times D) = A \times (B \times (C \times D))
\]

However, we still need to follow the order of matrix multiplication from left to right when computing the final result. The key points are:

1. Multiply \(A\) and \(B\), resulting in a new matrix.
2. Multiply \(C\) and \(D\), also resulting in a new matrix.
3. Multiply the two resulting matrices from steps 1 and 2 together.

### Relative Questions
1. What are the dimensions of matrices \(A\), \(B\), \(C\), and \(D\)?
2. What properties do we need to check before multiplying matrices?
3. Can matrix multiplication be commutative?
4. How do we compute the product of two matrices step-by-step?
5. What happens if the matrices have incompatible dimensions for multiplication?

### Tip:
Always ensure that the number of columns in the first matrix matches the number of rows in the second matrix for valid matrix multiplication.

Explore the associative property of matrix multiplication through the expression (A×B)×(C×D). Learn how to approach this problem, understand the key concepts like the associative property, and ensure proper dimension matching for matrix multiplication. Suitable for advanced high school and college students.

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