# Matrices: Transpose and Inverse

1. Nov 20, 2012

### PotentialE

1. The problem statement, all variables and given/known data
Find (X * Y-1)T - (Y * X-1)T
When X = [3 5]
..............[1 2]
and Y = [3 4]
...........[2 3]

2. Relevant equations
........................[-c a]

3. The attempt at a solution
I got:
[9 -6 ]
[14 -9]

[-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?

2. Nov 20, 2012

### haruspex

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

3. Nov 20, 2012

### 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

4. Nov 20, 2012

### hotvette

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

5. Nov 20, 2012

### PotentialE

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

6. Nov 20, 2012

### haruspex

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