Use row reduction to find the inverse of the given matrix if

Use row reduction to find the inverse of the given matrix if it exists, and check your answer by multiplication. [1 1 1 -1 0 -1 -1 -1 1]

Solution

Your matrix

Determinant is not zero, therefore inverse matrix exists

Very detailed solution  

Write the augmented matrix

Find the pivot in the 1st column in the 1st row

Eliminate the 1st column

Find the pivot in the 2nd column in the 2nd row

Eliminate the 2nd column

Make the pivot in the 3rd column by dividing the 3rd row by 2

Eliminate the 3rd column

There is the inverse matrix on the right

inverse =

	A1	A2	A3
1	1	1	1
2	-1	0	-1
3	-1	-1	1