### (AB)C = (AC)B

### The statement “(AB)C = (AC)B” is not universally true.

The statement “(AB)C = (AC)B” is not universally true. In general, the order of matrix multiplication does not commute, which means that the product of two matrices may depend on the order in which they are multiplied.

To illustrate this, consider the following example:

Let A be a 2×2 matrix, B be a 2×3 matrix, and C be a 3×4 matrix. In this case, (AB)C represents the product of matrices AB first, and then multiplying the result by C. On the other hand, (AC)B represents the product of matrices AC first, and then multiplying the result by B.

**The dimensions of the resulting matrices will differ:**

For (AB)C, the dimensions of AB will be 2×3, and multiplying it by C (3×4) will result in a matrix with dimensions 2×4.

For (AC)B, the dimensions of AC will be 2×4, and multiplying it by B (2×3) will result in a matrix with dimensions 2×3.

Since the resulting matrix dimensions are not the same, (AB)C cannot be equal to (AC)B in general.

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