I want to find the inverse of 2-i-2j+k
I know we want ab=1
Let a = 2 - i - 2j + k. Let b = x + yi + zj + wk. Work out a times b. This gives us the four equations:
2x + y + 2z - w = 1
-x + 2y -z - 2w = 0
-2x + y + 2z + w = 0
x + 2y - z + 2w = 0
The determinant of this coefficient matrix is not 0, so an inverse does exist. So solve the system.
-Dan