Determinant of Diagonal Matrix

Theorem
Let $$\mathbf{A} = \begin{bmatrix} a_{11} & 0 & \cdots & 0 \\ 0 & a_{22} & \cdots & 0 \\ \vdots & \vdots & \ddots & \vdots \\ 0 & 0 & \cdots & a_{nn} \\ \end{bmatrix}$$ be a diagonal matrix.

Then the determinant of $$\mathbf{A}$$ is the product of the elements of $$\mathbf{A}$$.

That is, $$\det \left({\mathbf{A}}\right) = \prod_{i=1}^n a_{ii}$$.

Proof
As a diagonal matrix is also a triangular matrix (both upper and lower), the result follows directly from Determinant of a Triangular Matrix.