Final answer:
The products of two matrices can be calculated by ensuring that the number of columns in the first matrix matches the number of rows in the second matrix. For both given matrices a and b, which are square 3x3 matrices, it is possible to find the products ab and ba through the dot product method of matrix multiplication.
Step-by-step explanation:
To calculate the product of two matrices, we must ensure that the number of columns in the first matrix is equal to the number of rows in the second matrix.
Matrix a is a 3x3 matrix, and matrix b is also a 3x3 matrix, so we can find both ab and ba because these matrices are square and of the same dimensions.
The product of matrices is found by multiplying the rows of the first matrix by the columns of the second matrix. If we denote matrix a and matrix b as follows:
Matrix a:
2 2 3
-3 -2 5
-1 1 2
Matrix b:
-1 0 -4
-4 2 -2
3 1 1
The matrix ab can be calculated by taking the dot product of each row of a with each column of b, and similarly, ba is calculated by taking the dot product of each row of b with each column of a.