#### Answer

The product of two matrices is not defined when the number of columns of the first matrix is not equal to the number of rows of the second matrix.

#### Work Step by Step

The product of two matrices is defined as follows:
Consider a matrix A of $m\times n$ order and another matrix B of $n\times k$ order.
To find the ${{i}^{th}}$ row and ${{j}^{th}}$ column of the product AB, each element in the ${{i}^{th}}$ row of the matrix A is multiplied by the corresponding element in the ${{j}^{th}}$ column of the matrix B, and then obtained products of corresponding elements are added.
The product matrix AB is an $m\times k$ order matrix, that is, if $A={{\left[ {{a}_{ij}} \right]}_{m\times n}}$ and $B={{\left[ {{b}_{jk}} \right]}_{n\times k}}$, then:
$\begin{align}
& AB=C \\
& C={{\left[ {{c}_{ik}} \right]}_{m\times k}}
\end{align}$
Here, ${{c}_{ik}}=\sum\limits_{j=1}^{n}{{{a}_{ij}}{{b}_{jk}}}$
Let $A={{\left[ \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right]}_{2\times 2}}$ and $X={{\left[ \begin{matrix}
k & n \\
l & o \\
m & p \\
\end{matrix} \right]}_{3\times 2}}$
Then,
$AX={{\left[ \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right]}_{2\times 2}}{{\left[ \begin{matrix}
k & n \\
l & o \\
m & p \\
\end{matrix} \right]}_{3\times 2}}$ is not possible because the element a is multiplied with k and b with l, but there is no element left in the first row of matrix A to be multiplied with element m of the matrix X.
Similarly, the element c is multiplied with n and d with o, but there is no element left in first row of matrix A to be multiplied with m of the matrix X.