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

1 Answer
Jul 16, 2016

Answer:

#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#.