Matrices: Transpose and Inverse

[PotentialE]

Homework Statement

Find (X * Y^-1)^T - (Y * X^-1)^T
When X = [3 5]
.....[1 2]
and Y = [3 4]
...[2 3]

Homework Equations

Inverse= 1/ad-bc [d -b]
......[-c a]

The Attempt at a Solution

I got:
[9 -6 ]
[14 -9]

But the answer is:
[-3 -2]
[6 3]I did the problem twice and got the same answer so I don't think its a simple math error, any insight as to how to solve this correctly / what I've done wrong?

 

[haruspex]

It's rather hard to say where you've gone wrong without seeing your working. Your equations are correct.

 

[PotentialE]

Well first I did the inverse of Y and got:
[3 -4]
[-2 3]

Then I multiplied that by X and got:
[5 7]
[-3 -4]

Then I transposed it and got:
[5 -3]
[7 -4]

Then I did the inverse of X and got:
[2 -5]
[-1 3]

Multiplied by Y and got:
[-4 -7]
[3 5]

Then I transposed that and got:
[-4 3]
[-7 5]

Then I subtracted the two transposed matrices to get:
[9 -6]
[14 -9]

Seems coherent to me but it's very far from the right answer

 

[hotvette]

In your second step, looks like you did Y^-1*X instead of X*Y^-1

 

[PotentialE]

Oh that's right! I forgot the associative property is non-applicable to matrices. THanks for your help.

 

[haruspex]

I forgot the associative property is non-applicable to matrices.

No, matrices are associative, A(BC) = (A B)C, but they are not always commutative.