Why isn't this working? a simple inverse of a 2x2 matrix

[mr_coffee]

Okay i have a simple problem, and its not working!
I have the following:
Find a 2x2 matrix
A =
-5 3
2 -9

A-1 =
-3/13 -1/13
2/39 -5/39

A*A-1 = I
1 0
0 1

but its saying the inverse i got is wrong! how is this?
det i got was 1/39

 

[amcavoy]

Okay i have a simple problem, and its not working!
I have the following:
Find a 2x2 matrix
A =
-5 3
2 -9

A-1 =
-3/13 -1/13
2/39 -5/39

A*A-1 = I
1 0
0 1

but its saying the inverse i got is wrong! how is this?
det i got was 1/39

Your determinant is actually 39 (not 1/39). Divide the adjoint matrix by that and you should get your answer (provided you calculated the adjoint correctly).

 

[mr_coffee]

thanks for the responce! But how did u get a det of -39? if a determinant is defined as
1/(ad-bc)?
so if i had
-5 3
2 -9

(-5)(-9) -(3)(2) = 45 - 6 = 39, and its under 1, so 1/39?
I also tried ur answer, when u say divide the adjoint matrix, do u mean divide the matrix after switching a and d, and negating b and c? I tried that and it was also wrong with ur det

 

[amcavoy]

thanks for the responce! But how did u get a det of -39? if a determinant is defined as
1/(ad-bc)?
so if i had
-5 3
2 -9

(-5)(-9) -(3)(2) = 45 - 6 = 39, and its under 1, so 1/39?
I also tried ur answer, when u say divide the adjoint matrix, do u mean divide the matrix after switching a and d, and negating b and c? I tried that and it was also wrong with ur det

The determinant of a 2x2 matrix is ad-bc. I meant to say 39, not -39.

 

[TD]

thanks for the responce! But how did u get a det of -39? if a determinant is defined as
1/(ad-bc)?

No!

The inverse is 1/det(A) * adj(A) where 1/det(A) = 1/(ad-bc) so det(A) = ad-bc and not 1/(ad-bc).