SOLUTION: Are these matrices inverses of each other? Show why or why not. [2 -1] [-3 1] [-1 -1] [-3 -2]

Algebra ->  Matrices-and-determiminant -> SOLUTION: Are these matrices inverses of each other? Show why or why not. [2 -1] [-3 1] [-1 -1] [-3 -2]      Log On


   

Question 176155: Are these matrices inverses of each other? Show why or why not.

[2 -1]
[-3 1]

[-1 -1]
[-3 -2]
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The inverse of a 2x2 matrix [A], where
[A]=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29
is given by
[A]inv=DELTA%2A%28matrix%282%2C2%2Cd%2C-b%2C-c%2Ca%29%29
where
DELTA=1%2F%28ad-bc%29
In your case,
a=2
b=-1
c=-3
d=1
DELTA=1%2F%282%281%29-%28-1%29%28-3%29%29
DELTA=1%2F%282-3%29
DELTA=-1
[A]inv=%28-1%29%2A%28matrix%282%2C2%2C1%2C1%2C3%2C2%29%29
[A]inv=%28matrix%282%2C2%2C-1%2C-1%2C-3%2C-2%29%29
This matrix matches the inverse given.
Yes, they are inverses.