Introduction:
The question asks about the properties of multiplication of real-valued square matrices of the same dimension. We need to determine which of the given options correctly describes the properties of matrix multiplication.

Explanation:
Matrix multiplication is an operation that combines two matrices to produce a new matrix. Let's analyze each option to determine its correctness:

a) Not always possible to compute:
This option is incorrect because the multiplication of real-valued square matrices of the same dimension is always possible to compute. The resulting matrix will have the same dimensions as the original matrices, and each element of the resulting matrix is computed by taking the dot product of the corresponding row of the first matrix and the corresponding column of the second matrix.

b) Associative:
Matrix multiplication is associative, which means that for three matrices A, B, and C of appropriate dimensions, (AB)C = A(BC). This property allows us to change the grouping of matrices in a multiplication expression without changing the final result. Hence, this option is correct.

c) Always positive definite:
Positive definiteness is a property that applies to square matrices in the context of linear algebra. It is not a property of matrix multiplication. Therefore, this option is incorrect.

d) Commutative:
Commutativity means that the order of the operands does not affect the result. However, matrix multiplication is not commutative. In general, AB ≠ BA for square matrices A and B. The order of multiplication matters in matrix multiplication, and changing the order of multiplication will yield different results. Therefore, this option is incorrect.

Summary:
In conclusion, the correct option is 'b) Associative'. Matrix multiplication of real-valued square matrices of the same dimension is always possible to compute and follows the associative property. It is not always positive definite and not commutative.