How do you solve this matrix?

Question

I have this 2x2 matrix, which is multiplied by another 2x2 matrix.
| A B| Multiplied by | X Y| Which Equals | 1 0 |
| C D| Multiplied by | Z W| Which Equals | 0 1 |

How do I go about solving X, Y, Z, and W in terms of A, B, C, and D?

Thanks for the help!

I meant to write...
[A B
C D] abcd is Maxtrix A.

[X Y
Z W] xyzw is Matrix B.

Matrix A times Matrix B equals the matrix of

[1 0
0 1] 1001.

Hope that helps.

Answer 1

Since the answer when you multiply is the identity matrix, the matrices must be inverses of each other.

The inverse of
[ A B]
[C D]
is
( [ D -B ]
[-C A ] ) / (AD - BC)
So ...
X = D/(AD - BC)
Y = -B/(AD - BC)
Z = -C/(AD - BC)
W = A/(AD - BC)

... By the way, AD - BC is just the determinant of the first matrix.

Answer 2

The two equations are independent of each other. Terms in equation 1, A,B, and X,Y, do not appear in the second equation as you have presented. It is a indeterminate problem.