Question

does the given matrix, A, have an inverse? if it does what is A^-1?

Answer 1

\(\large {
\textit{inverse of a 2x2 matrix}
\\ \quad \\

A=
\begin{bmatrix}
a&{\color{brown}{ b}}\\c&{\color{brown}{ d}}
\end{bmatrix}\qquad A^{-1}=\cfrac{1}{a\cdot {\color{brown}{ d}}-c\cdot {\color{brown}{ b}}}
\begin{bmatrix}
{\color{brown}{ d}}&-{\color{brown}{ b}}\\-c&a
\end{bmatrix}
}\)

Answer 2

okay so the inverse would be..