inverse values in matrices?

Question

ok more matrices....
say X is equal to
1 3 3
1 3 4
1 4 3
and Y is equal to
7 -3 a
b 0 1
-1 1 0
i need to determine the values of a, b such that Y is the inverse of X, that is XY= the identity matrix I subscript 3
so if i multiply YX it has to equal
1 0 0
0 1 0
0 0 1
???
i'm not sure if i'm understanding the question properly =(
thank you if anyone can help........

Answer 1

Matrix multiplication XY, should Y be a near-inverse, should yield the identity matrix. Remember how matrix multiplication works; multiplying the 1st row of X with the 1st column of Y should yield a result of 1, since the 1st row, 1st column of the identity matrix is 1. This means

1(7) + 3(b) + 3(-1) = 1
7 + 3b - 3 = 1
4 + 3b = 1
3b = -3
b = -1

If we take the first row of X and the 3rd column of Y, we should get an answer of 0, since entry (1, 3) in the identity matrix is 0. Therefore,

1(a) + 3(1) + 3(0) = 0
a + 3 = 0
a = -3

And there you have it;
a = -3, b = -1