Answer
The statement does not make sense. The correct statement is, “The $m\times n$ matrix and an $n\times p$ matrix are multiplied by multiplying corresponding elements and then adding them.”
Work Step by Step
The product of two matrices is defined as below:
Consider a matrix A of $m\times n$ order and another matrix B of $n\times p$ order.
To find the ${{i}^{th}}$ row and ${{j}^{th}}$ column of the product AB, each element in the ${{i}^{th}}$ row of A is multiplied by the corresponding element in the ${{j}^{th}}$ column of B, and then these products are added.
The product matrix AB is an $m\times p$ order matrix, that is, if $A={{\left[ {{a}_{ij}} \right]}_{m\times n}}$ and $B={{\left[ {{b}_{jp}} \right]}_{n\times p}}$, then
$\begin{align}
& AB=C \\
& C={{\left[ {{c}_{ip}} \right]}_{m\times p}}
\end{align}$
Here, ${{c}_{ip}}=\sum\limits_{j=1}^{n}{{{a}_{ij}}{{b}_{jp}}}$
Let $A={{\left[ \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right]}_{2\times 2}}$ and $X={{\left[ \begin{matrix}
x \\
y \\
\end{matrix} \right]}_{2\times 1}}$, then
$\begin{align}
& AX={{\left[ \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right]}_{2\times 2}}{{\left[ \begin{matrix}
x \\
y \\
\end{matrix} \right]}_{2\times 1}} \\
& ={{\left[ \begin{matrix}
ax+by \\
cx+dy \\
\end{matrix} \right]}_{2\times 1}}
\end{align}$
The matrix multiplication cannot be performed by simply multiplying the elements. The elements are then added.
Therefore, the statement does not make sense. The correct statement is, “The $m\times n$ matrix and an $n\times p$ matrix are multiplied by multiplying corresponding elements and then adding them.”
