Thread: Matrix Algebra - fairly basic

Using the definition of the inverse of a matrix and the principles of matrix algebra, prove that if A and B are invertible matrices of the same order, then AB is invertible and = .

Please help.

Originally Posted by WWTL@WHL

Using the definition of the inverse of a matrix and the principles of matrix algebra, prove that if A and B are invertible matrices of the same order, then AB is invertible and = .

Please help.

Hint: recall that if a matrix is invertible, and we denote as its inverse matrix, then and

here, we simply need to show that , and the desired result follows immediately. use the fact that if are matrices, then

Yes, that makes sense. But I don't understand why you'd need to use this fact . How does that relate to the ?

Could you please expand on this a bit more, or give a more detailed explanation please? I am really, really poor at maths.

Thanks.

Originally Posted by WWTL@WHL

Yes, that makes sense. But I don't understand why you'd need to use this fact . How does that relate to the ?

Could you please expand on this a bit more, or give a more detailed explanation please?

i give you one more hint.

Consider

in light of the fact that i told you to note (it would also do you well to recall the properties of the identity matrix), we will have that:

I am really, really poor at maths.

you and me both

It looks like I've committed a mathematical sin there, and I don't think I've got anywhere.

Just realised I^2 = I!! Thanks, I think I've got it.

Thanks so much Jhevon!!!

Originally Posted by WWTL@WHL

It looks like I've committed a mathematical sin there, and I don't think I've got anywhere.

i told you to recall the properties of the identity matrix.

Definition: If we have a matrix, , such that for any matrix , then we call the identity matrix. It is a matrix of the same order of with a diagonal of 's on it's main diagonal and 0's everywhere else. Multiplying any matrix by the identity matrix gives the original matrix itself

in other words:

Originally Posted by Jhevon

i told you to recall the properties of the identity matrix.

Definition: If we have a matrix, , such that for any matrix , then we call the identity matrix. It is a matrix of the same order of with a diagonal of 's on it's main diagonal and 0's everywhere else. Multiplying any matrix by the identity matrix gives the original matrix itself

in other words:

Yes - of course.

Thank you so much for your patience, and I'm sorry you had to walk me through this one. I really should've understood it. I'm only 2 weeks in to my maths course at university, and I'm already stuggling. Ho-hum.....

Originally Posted by WWTL@WHL

Yes - of course.

Thank you so much for your patience, and I'm sorry you had to walk me through this one. I really should've understood it. I'm only 2 weeks in to my maths course at university, and I'm already stuggling. Ho-hum.....

that's fine. i understand what it is to struggle with math, really. now can you complete the proof?

Originally Posted by Jhevon

that's fine. i understand what it is to struggle with math, really. now can you complete the proof?

Yep.

Originally Posted by WWTL@WHL

Yep.

good!

(you can post it if you want to make sure everything is in order)