Answer
TRUE
Work Step by Step
The determinate for a square matrix for $m$ columns anfd $n$ rows is defined as:
$det(A)= \begin{vmatrix}p&q\\r&s\end{vmatrix}=ps-rq$
Counter Example: $det(A)= \begin{vmatrix}2&3\\2&3\end{vmatrix}=(2)(3)-(3)(2)=6-6=0$
Therefore, the given statement is true that when $det(A)=0$, then the matrix $A$ is not invertible.