APFIVE Matrix Determinant and Inverse
I. For $$A=\begin{pmatrix}2 & 3 \\ 1 & 4\end{pmatrix}$$, the determinant is computed as $$2*4-3*1=5$$.
II. Since the determinant is nonzero, the matrix $$A$$ is invertible.
III. The inverse of $$A$$ is given by $$\frac{1}{5}\begin{pmatrix}4 & -3 \\ -1 & 2\end{pmatrix}$$.
Which of these statements about the matrix $$A$$ are true?
A
Only statements I and II are true.
B
Only statements II and III are true.
C
Statements I, II, and III are true.
D
Only statement I is true.
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