Find the inverse for the matrix?

Question

A= [-5 -2 -2
2 1 0
1 0 1]
B. Show your Candidate is the inverse. That is AA-1=A-1A=I

Answer 1

First find the adjoint matrix:

adj A:

1 0 2 1
0 1 1 0
-2 -2 -5 -2
1 0 2 1

1 -2 -1
2 -3 -2
2 -4 -1

1 2 2
-2 -3 -4
-1 -2 -1


Find determinant of original matrix:

detA = -5(1-0) -2(0-2) -2(0-1) = -5 + 4 + 2 = 1

The inverse matrix is adjA / detA = adjA / 1 = adjA

invA =
[
1 2 2
-2 -3 -4
-1 -2 -1
]

Answer 2

start by putting it into an augmented matrix, that is glue an identity matrix on to the side of it. like so

-5 -2 -2 1 0 0
2 1 0 0 1 0
1 0 1 0 0 1

now do all the proper row reductions to transform your original matrix into the identity matrix and what you end up with on the right hand side is going to be your inverse matrix

I'm not going to go through all the work here I hope you can do it on your own. I could just write the answer but then you wouldn't learn anything.

Answer 3

A^-1 =
[1 2 2]
[-2 -3 -4]
[-1 -2 -1]

Answer 4

thisshould help

http://mathworld.wolfram.com/MatrixInverse.html