Question

How do you find the inverse of `A=``((1, -1, 0), (0, 1, 0), (0, 0, 1))`?

Answer 1

`A^(-1) = ((1,1,0),(0,1,0),(0,0,1))`

Explanation:

`A^(-1) = ((1,1,0),(0,1,0),(0,0,1))`

Notice the effect of multiplying:

`A((a),(b),(c)) = ((1,-1,0),(0,1,0),(0,0,1))((a),(b),(c)) = ((a-b),(b),(c))`

To reverse the effect of subtracting `b` from `a` we need to add it. So all we need to do to form the inverse of `A` is to reverse the sign of the off diagonal `-1`.