Matrix Determinant and Inverse

Let matrix $A = \begin{pmatrix} 2 & 3 \\ 1 & 4 \end{pmatrix}$. Consider the following statements.

I. The determinant of $A$ is $(2)(4) - (3)(1) = 5$.

II. Matrix $A$ is invertible because its determinant is not equal to zero.

III. The inverse of $A$ is $A^{-1} = \frac{1}{5}\begin{pmatrix} 4 & -3 \\ -1 & 2 \end{pmatrix}$.

Which of the statements are true?