Find the inverse of the matrix [tex]\left[\begin{array}{cc}-4&6\\8&-12\\\end{array}\right][/tex]
if it exist.

Answer:
D
Step-by-step explanation:
If there is a 2x2 matrix as [tex]\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right][/tex]
The determinant is given by [tex]\frac{1}{ad-bc}\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right][/tex]
Now, if we calculate the value of "ad - bc", we see that:
[tex](-4)(-12)-(8)(6)=0[/tex]
We can't calculate the inverse, the inverse doesn't exist. The answer is D.