Answer:
[tex]\left[\begin{array}{ccc}1/17&-3/17\\3/34&4/17\\\end{array}\right][/tex]
Step-by-step explanation:
To find the inverse of a matrix you will need to compute [tex]\frac{1}{ad-bc}*\left[\begin{array}{ccc}a&b\\c&d\\ \end{array}\right] \\[/tex] which in this case will be [tex]\frac{1}{16 - (-18)}\left[\begin{array}{ccc}2&-6\\3&8\\\end{array}\right] = \frac{1}{34} \left[\begin{array}{ccc}2&-6\\3&8\\\end{array}\right] = \left[\begin{array}{ccc}2/34&-6/34\\3/34&8/34\\\end{array}\right][/tex] then reducing the fractions with in the matrix results in [tex]\left[\begin{array}{ccc}1/17&-3/17\\3/34&4/17\\\end{array}\right][/tex].
You can check to make sure your matrix is correct my multiplying by the original one and of you end up with the identity matrix then you know that your inverse is correct.