# Matrices: Transpose and Inverse

## 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?

## Answers and Replies

haruspex
Homework Helper
Gold Member
2020 Award
It's rather hard to say where you've gone wrong without seeing your working. Your equations are correct.

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

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

haruspex