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.
