Final answer:
The student's question involves proving the associativity of matrix multiplication by comparing the results of (AB)C and A(BC) to see if they yield the same matrix. Matrix multiplication is associative in linear algebra, unlike the anticommutative nature of vector cross products.
Step-by-step explanation:
The student is asking to verify whether matrix multiplication is associative with given matrices A, B, and C. To show this, one must compute both (AB)C and A(BC) and demonstrate that they result in the same matrix. Associativity means that no matter how we group the matrices during multiplication (as long as the order remains the same), the result will be the same.
First, we calculate AB, then multiply the resulting matrix by C as (AB)C. Then we compute BC, and multiply matrix A by the resulting matrix as A(BC). Comparing the final results of (AB)C and A(BC) will show if the multiplication is associative, as the products should be equal if matrix multiplication is indeed associative.
It's important to note that we are not considering any operations involving the cross product of vectors, which is anticommutative and does not apply to the concept of associativity in matrix multiplication. Associativity is a fundamental property of matrix multiplication in the context of linear algebra.