Answer
The provided statement is false.
Work Step by Step
The matrix $AX=B$ is determined if we consider the simultaneous equations.
$\begin{align}
& x+2y=4 \\
& 3x-5y=1 \\
\end{align}$
Now, write in matrix form as below,
Where,
$A=\left[ \begin{matrix}
1 & 2 \\
3 & -5 \\
\end{matrix} \right]$
$X=\left[ \begin{align}
& X \\
& Y \\
\end{align} \right]$
$B=\left[ \begin{align}
& 4 \\
& 1 \\
\end{align} \right]$
Now, solve the matrix $AX=B$
For X, multiply $A$ and the inverse of $B$, which is not possible. So, the statement is false.
There is a formula to find the $X$, $AX=B$.
Multiply both sides by the inverse of $A$.
${{A}^{-1}}AX={{A}^{-1}}B$
Where ${{A}^{-1}}A=I$ which is the identity matrix.
Therefore $IX=X$
So, $X={{A}^{-1}}B$. There is a formula for finding the value of $X$.
Then, the expression is true.
If A is invertible, it is not possible to solve the equation for X.
