1. The problem asks to understand what a singular matrix is. 2. A matrix $A$ is called singular if it does not have an inverse. 3. One key property: a matrix is singular if and only if its determinant is zero, i.e., $$\det(A) = 0.$$ 4. This means the matrix compresses space in some dimension, so there is no way to "undo" the transformation represented by $A$. 5. For example, for a 2x2 matrix $A = \begin{bmatrix}a & b \\ c & d\end{bmatrix}$, the determinant is $ad - bc$. 6. If $ad - bc = 0$, then matrix $A$ is singular. 7. A singular matrix does not have full rank; its rank is less than its size. 8. In conclusion, a singular matrix is one that satisfies $$\det(A) = 0,$$ which means it is not invertible.