Using the definition of the inverse of a matrix and the principles of matrix algebra, prove that ifAandBare invertible matrices of the same order, thenABis invertible and=.

Please help. :o

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- October 14th 2007, 10:43 AMWWTL@WHLMatrix 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. :o - October 14th 2007, 11:06 AMJhevon
- October 14th 2007, 11:15 AMWWTL@WHL
http://www.mathhelpforum.com/math-he...f4c54e40-1.gif

Yes, that makes sense. But I don't understand why you'd need to use this fact http://www.mathhelpforum.com/math-he...485a3abe-1.gif. How does that relate to the http://www.mathhelpforum.com/math-he...f4c54e40-1.gif ?

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

Thanks. - October 14th 2007, 11:19 AMJhevon
- October 14th 2007, 11:25 AMWWTL@WHL
http://www.mathhelpforum.com/math-he...9ea2dfed-1.gif

:confused:

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!!! :) - October 14th 2007, 11:30 AMJhevon
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: - October 14th 2007, 11:33 AMWWTL@WHL
- October 14th 2007, 11:45 AMJhevon
- October 14th 2007, 11:57 AMWWTL@WHL
- October 14th 2007, 12:00 PMJhevon