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To check if the multiplication of two matrices is defined, compare the number of columns of the first matrix with the number of rows in the second matrix. If the number of columns in the first matrix is equal to the number of rows in the second matrix, then the matrix multiplication is defined, otherwise it is not. Since both matrices A and B have the size 4x4, the number of columns in matrix A (4) is equal to the number of rows in matrix B (4). Therefore, the matrix multiplication AB is defined. Similarly, the number of columns in matrix B (4) is equal to the number of rows in matrix A (4), so the matrix multiplication BA is also defined.

Once we have confirmed that matrix multiplication is defined, we can determine the size of the product matrices. The size of a product matrix can be determined by combining the number of rows in the first matrix with the number of columns in the second matrix. For the multiplication AB, we take the number of rows from matrix A (4) and the number of columns from matrix B (4), which gives us a product matrix AB with the dimensions 4x4. Similarly, for the multiplication BA, we take the number of rows from matrix B (4) and the number of columns from matrix A (4), which also gives us a product matrix BA with the dimensions 4x4. In conclusion, both matrix products AB and BA are defined, and both have a size of \(4 \times 4\).