Why is a non-invertible matrix called a singular matrix?

For $T\in M_{n,n}(\mathbb{C})$$T\in M_{n,n}(\mathbb C )$, if $detT=0$$\det T= 0$, then we say $T$$T$ is a singular matrix.

Sometimes, for a function $\frac{1}{f}$$\frac{1}{f}$, if $f(t)=0$$f(t)=0$, we will say that $t$$t$ is a singular point of $\frac{1}{f}$$\frac{1}{f}$, or $f\in {\mathfrak{m}}_t$$f\in \mathfrak{m}_t$.

What is the connection between these two concept?

Notice that $det(-):M_{n,n}(\mathbb{C})\cong {\mathbb{C}}^{n\times n}\to \mathbb{C}$$\det(-):M_{n,n}(\mathbb C)\cong\mathbb C^{n\times n}\to\mathbb C$ is a polynomial function.

Hence consider the function $\begin{array}{c}h(-)=\frac{1}{det(-)}\end{array}$$h(-)=\frac{1}{\det(-)}\\$, the singular matrix is the singular point of $h(-)$$h(-)$.