Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together.  To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix.  For this example, our product matrix will have dimensions of (3x3). The product matrix equals, 

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together.  To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix.  For this example, our product matrix will have dimensions of (1x1). 

In order to be able to multiply matrices, the number of columns of the 1st matrix must equal the number of rows in the second matrix.  Here, the first matrix has dimensions of (1x3). This means it has one row and three columns.  The second matrix has dimensions of (1x3), also one row and three columns.  Since , we cannot multiply these two matrices together

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together.  To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix.  For this example, our product matrix will have dimensions of (3x2). The product matrix equals, 

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together.  To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix.  For this example, our product matrix will have dimensions of (1x3). The product matrix equals, 

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together.  To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix.  For this example, our product matrix will have dimensions of (2x1). The product matrix equals, 

Since the number of columns in the first matrix does not equal the number of rows in the second matrix, you cannot multiply these two matrices. 

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together.  To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix.  For this example, our product matrix will have dimensions of (2x2). The product matrix equals, 

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together.  To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix.  For this example, our product matrix will have dimensions of (1x4). The product matrix equals, 

Since the number of columns in the first matrix equals the number of rows in the second matrix, we know that these matrices can be multiplied together.  To determine the dimensions of the product matrix, we take the number of rows in the first matrix and the number of columns in the second matrix.  For this example, our product matrix will have dimensions of (3x1). The product matrix equals,