Question

Directions:

Does the following inverse of [2 6 exist?
1 3]

If it isn't an inverse, explain why.

Answer 1

The inverse of a 2x2 matrix is given by:
A=[a b A^1=1/ad-bc[d -b
c d]. -c a].
If these two multiplied by each other gives the "identity matrix": [1 0
0 1].
then the inverse exists.

Answer 2

The determinant

|2 6|
|1 3| = 6-6 = 0
So, there is no inverse