The inverse of the matrix
is represented by the matrix
.
<h3>How to determine the inverse matrix</h3>
A matrix <em>A</em> has an <em>inverse</em> matrix if and only if its determinant is different than 0. Given that we have a matrix formed by 2 rows and 2 columns, we can obtain the following <em>inverse</em> matrix by using the following formula:
(1)
Where
is the adjoint of the matrix, which is the transposed of the <em>cofactor</em> matrix.
If we know that
, then the inverse of the matrix is determined below:

![adj (\vec A) = \left[\begin{array}{cc}4&-2\\-3&1\end{array}\right]](https://tex.z-dn.net/?f=adj%20%28%5Cvec%20A%29%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-2%5C%5C-3%261%5Cend%7Barray%7D%5Cright%5D)
![\vec A^{-1} = -\frac{1}{2}\cdot \left[\begin{array}{cc}4&-2\\-3&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cvec%20A%5E%7B-1%7D%20%3D%20-%5Cfrac%7B1%7D%7B2%7D%5Ccdot%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D4%26-2%5C%5C-3%261%5Cend%7Barray%7D%5Cright%5D)
![\vec A^{-1} = \left[\begin{array}{cc}-2&1\\\frac{3}{2} &-\frac{1}{2} \end{array}\right]](https://tex.z-dn.net/?f=%5Cvec%20A%5E%7B-1%7D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2%261%5C%5C%5Cfrac%7B3%7D%7B2%7D%20%26-%5Cfrac%7B1%7D%7B2%7D%20%5Cend%7Barray%7D%5Cright%5D)
The inverse of the matrix
is represented by the matrix
. 
To learn more on matrices, we kindly invite to check this verified question: brainly.com/question/11367104