Thread: Help with a Linear Algebra - Matrices assignment..

1. Help with a Linear Algebra - Matrices assignment..

Hi There,

I've just been handed an assignment that I have no clue how to do..

I will show you some of the questions below but I am not looking for straight answers. I would like some pointers on how to go about solving these where to get help.

Introduction
Show if the folowing statements are true or false for 2 x 2 matrices.

1)
det(AB) = det(A)det(B)
2)
det(A^-1)= 1(over)det(A)
3)
det(A^T)=det(A)

Any advice would be greatly appreciated as this is due in one week and I have no clue how to go about this?

Thanks..

2. Originally Posted by atwarwithmaths
Hi There,

I've just been handed an assignment that I have no clue how to do..

I will show you some of the questions below but I am not looking for straight answers. I would like some pointers on how to go about solving these where to get help.

Introduction
Show if the folowing statements are true or false for 2 x 2 matrices.

1)
det(AB) = det(A)det(B)
2)
det(A^-1)= 1(over)det(A)
3)
det(A^T)=det(A)

Any advice would be greatly appreciated as this is due in one week and I have no clue how to go about this?

Thanks..
Define

$\displaystyle A = \left[\begin{matrix}a_{11} & a_{12} \\ a_{21} & a_{22}\end{matrix}\right]$ and $\displaystyle B = \left[\begin{matrix}b_{11} & b_{12}\\b_{21} & b_{22}\end{matrix}\right]$

Find $\displaystyle AB, A^{-1}\textrm{ and }A^T$ and then you can find the appropriate determinants and see if your statements hold true.