Chapter 5 - Section 5.7 - Properties of Matrices - 5.7 Exercises - Page 554: 60

The size of matrix $A$ is $2 \times 4$ and that of matrix $B$ is $2 \times 3$. This shows that the number of columns of matrix-$A$ is not same as the number of rows of the matrix-$B$. So, their product $AB$ does not exist.

Let us consider two matrices $A$ and $B$ and their multiplication can be possible when the number of columns of matrix-$A$ is the same as the number of rows of the matrix-$B$. We can see from the given matrices that the size of matrix $A$ is $2 \times 4$ and that of matrix $B$ is $2 \times 3$. This shows that the number of columns of matrix-$A$ is not same as the number of rows of the matrix-$B$. So, the product $AB$ does not exist.