Answer
The provided statement is False.
Work Step by Step
The inverse of a $2\times 2$ matrix is determined as below:
$A=\left[ \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right]$
$B=\left[ \begin{matrix}
e & f \\
g & h \\
\end{matrix} \right]$
Now, we will consider that the multiplication equals,
$\left[ AB \right]=\left[ \begin{matrix}
p & q \\
r & s \\
\end{matrix} \right]$
Then, the inverse is
${{\left[ AB \right]}^{-1}}=\frac{1}{ps-qr}\left[ \begin{matrix}
s & -r \\
-q & p \\
\end{matrix} \right]$
Thus, the matrix is invertible. If $ad-bc\ne 0$, then it is not.
