Question

Find the inverse of the matrix
`\left[\begin{array}{cc}-4&6\\8&-12\\\end{array}\right]`

if it exist.

Answer 1

D

Explanation:

If there is a 2x2 matrix as
`\left[\begin{array}{ccc}a&b\\c&d\\\end{array}\right]`

The determinant is given by
`(1)/(ad-bc)\left[\begin{array}{ccc}d&-b\\-c&a\\\end{array}\right]`

Now, if we calculate the value of "ad - bc", we see that:

`(-4)(-12)-(8)(6)=0`

We can't calculate the inverse, the inverse doesn't exist. The answer is D.