Question

the inverse of A = 2 -1

Answer 1

sorry

Answer 2

i mean the inverse of A = 2 -1
3 5
so how do i solve for A?

Answer 3

to find inverse of
\[\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\]
you do
\[\frac{1}{ad-bc}*\left[\begin{matrix}d & -b \\ -c & a\end{matrix}\right]\]

also if ad-bc=0, the inverse does not exist

i will now prove these two are inverses:

\[\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]*\left[\begin{matrix}\frac{d}{ad-bc} & \frac{-b}{ad-bc} \\ \frac{-c}{ad-bc} & \frac{a}{ad-bc}\end{matrix}\right]\]
\[\left[\begin{matrix}\frac{ad-bc}{ad-bc} & \frac{-ab+ab}{ad-bc} \\ \frac{cd-cd}{ad-bc} & \frac{-cb+ad}{ad-bc}\end{matrix}\right]=\left[\begin{matrix}1 & 0 \\ 0& 1\end{matrix}\right]\]
which is the identity matrix so thus we have proved they are inverses

Answer 4

looking at your matrix we have the inverse is:
\[\frac{1}{2(5)-(-1)(3)}*\left[\begin{matrix}5 & 1 \\ -3 & 2\end{matrix}\right]\]