Answer:
[tex]\left[\begin{array}{cc}-\frac{1}{2}&\frac{1}{6}\\-\frac{1}{2}&\frac{1}{3}\\\end{array}\right][/tex]
Step-by-step explanation:
If a 2x2 matrix is given as:
[tex]\left[\begin{array}{cc}a&b\\c&d\\\end{array}\right][/tex]
The inverse is:
[tex]\frac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right][/tex]
Our matrix given is:
[tex]\left[\begin{array}{cc}-4&2\\-6&6\\\end{array}\right][/tex]
Using the formula, let's find the inverse:
[tex]\frac{1}{ad-bc}\left[\begin{array}{cc}d&-b\\-c&a\\\end{array}\right]\\=\frac{1}{(-4)(6)-(-6)(2)}\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\frac{1}{-12}\left[\begin{array}{cc}6&-2\\6&-4\\\end{array}\right]\\=\left[\begin{array}{cc}-\frac{1}{2}&\frac{1}{6}\\-\frac{1}{2}&\frac{1}{3}\\\end{array}\right][/tex]
