Inverse of given matrix is [tex]\frac{1}{5} \left[\begin{array}{ccc}2&-3\\1&1\\\end{array}\right][/tex]
What is inverse of given matrix ?
Given matrix is A = [tex]\left[\begin{array}{ccc}1&3\\-1&2\\\end{array}\right][/tex]
Determinant of A = detA = (1×2)-(-1)(3) = 2-(-3)=2+3=5≠0
Since, detA≠0, we can say that, [tex]A^{-1}[/tex] exists.
adj(A) = [tex]\left[\begin{array}{ccc}2&-3\\1&1\\\end{array}\right][/tex]
∴ [tex]A^{-1} =\frac{1}{detA} adj(A)[/tex]
[tex]=\frac{1}{5} \left[\begin{array}{ccc}2&-3\\1&1\\\end{array}\right][/tex]
So, the 4th option is correct.
Learn more about matrix inverse here :
https://brainly.com/question/12440283
#SPJ2
