Answer
The statement is false.
To make it true, after the text
" All square 2$\times$2 square matrices ... "
insert the following:
" ... $\left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right]$, such that $ad-bc\neq 0$ , ..."
Work Step by Step
The matrix $A$ is invertible if and only if $ad-bc\neq 0$.
If $ad-bc=0$, then $A$ does not have a multiplicative inverse.
If $A=\left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right]$, then $A^{-1}=\displaystyle \frac{1}{ad-bc}\left[\begin{array}{ll}
d & -b\\
-c & a
\end{array}\right]$.
So, not all 2$\times$2 matrices have an inverse.
The statement is false.
To make it true, after the text
" All square 2$\times$2 square matrices"
insert the following:
" ... $\left[\begin{array}{ll}
a & b\\
c & d
\end{array}\right]$, such that $ad-bc\neq 0$ ..."
