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.