Answer to Question #211529 in Linear Algebra for Moe

Question

Let $B = \begin{pmatrix} 1 & 0 \\ 2 & 3 \end{pmatrix}$

What is B^-1?

Answer 1

Given $\begin{pmatrix} 1& 0 \\ 2 & 3 \end{pmatrix}$

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

$A^{-1}=\frac{1}{ad-bc}\begin{pmatrix} d &- b \\ - c & a \end{pmatrix}$

$B^{-1}=\frac{1}{1×3-2×0}\begin{pmatrix} 3 & 0 \\ -2 & 1 \end{pmatrix}$

$B^{-1}=\frac{1}{3}\begin{pmatrix} 3 & 0\\ -2 & 1 \end{pmatrix}$

$B^{-1}=\begin{pmatrix} 1 & 0 \\ \frac{-2}{3} & \frac{1}{3} \end{pmatrix}$