Question

Could someone explain to me how to solve this problem step by step?

Find the inverse of A= [2 4]
[3 5]

Answer 1

first find determinant of this matrix such as 5*2- 3*4 = -2
then multiply this matrix by reciprocal of this number which is -1/2. But, you need to change the sign of 4 and 3 to negative before you multiply it. Inverse of this matrix must be.

[-1 2]
[3/2 -5/2]

Answer 2

\[A=\left[\begin{array}{cc}
2 & 4\\3 & 5
\end{array}\right]\]\[A^{-1}=\frac{1}{\det{A}}adj{A}=\frac{1}{-2}\left[\begin{array}{cc}
5 & -3\\-4 & 2
\end{array}\right]^T=\frac{1}{-2}\left[\begin{array}{cc}
5 & -4\\-3 & 2
\end{array}\right]\]\[A^{-1}=\left[\begin{array}{cc}
-2.5 & 2\\1.5 & -1
\end{array}\right]\] http://www.wolframalpha.com/input/?i=inverse+of+%28%282%2C4%29%2C%283%2C5%29%29