Mathematics

Problem

For the matrix

A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}

with

ad-bc \neq 0

, which of the following correctly represents

A^{-1}

? a)

\dfrac{1}{ad-bc}\begin{pmatrix} a & -c \\ -b & d \end{pmatrix}

\dfrac{1}{ad-bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}

\dfrac{1}{bc-ad}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}

\dfrac{1}{ad+bc}\begin{pmatrix} d & -b \\ -c & a \end{pmatrix}