Question

Does every matrix have a determinant?

Answer 1

Explanation for the answer:

The determinant only exists for square matrices.

Every SQUARE matrix $n\times n$ has a determinant.
The determinant $\left|A\right|$ of a square matrix $A$ is a number that helps you to decide what kind of solutions a system can have unique, no solutions or an infinite number of solutions.

So, every matrix does not have a determinant.