Linear Algebra Proof: if A satisfies the equation A^2 -7a + I = 0 then find A^-1

[BLackcuts]

2 Questions

if A satisfies the equation A^2 -7a + I = 0 then find A^-1

Next one is

If A is an invertible matrix show that AA^T and A^TA are invertible and find theirinverses.

 

[Deleted member 4993]

2 Questions

if A satisfies the equation A^2 -7a + I = 0 then find A^-1

Next one is

If A is an invertible matrix show that AA^T and A^TA are invertible and find theirinverses.

Please post one problem in one post.

Please include your work, explaining exactly where you are stuck.

 

[stapel]

1. If A satisfies the equation A^2 -7a + I = 0, then find A^-1

How does your book define "a"? For instance, if it's a scalar (which would be its normal interpretation, in context), then I'm not sure what you're supposed to do with it, since the equation makes no sense. :shock:

2. If A is an invertible matrix, show that AA^T and A^TA are invertible and find their inverses.

You are given that A is invertible, so you know that A^-1 exists, and such that AA^-1 = A^-1A = I. Past this, however, we can't know what other results you have. For instance, have you been given the result (d) of page 9 of this PDF document?

When you reply, please include a clear listing of all of your thoughts and efforts so far, along with whatever theorems, definitions, results, etc, from class that you feel may apply, so we know what's available to you. Thank you!