Is there some special method to find the inverse of an elementary matrix?

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Is there some special method to find the inverse of an elementary matrix?

Mathematics
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haha u r here without a notification
Gaussian Row-Reduction is useful. For a two by two matrix, \[A =\left[\begin{matrix}a & b \\ c & d\end{matrix}\right]\] The inverse matrix is \[\frac{1}{ad-bc} \left[\begin{matrix}d & -b\\ -c &a\end{matrix}\right]\]
i think they are looking for something using elementary row operations

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I mean elentary matrices
I don't know what you mean by an elementary matrix.
LOL neither do I ok i will read some more and try to figure oout
Oh oh oh nevermind, sorry, my fault. You only need one row operation to change an elementary matrix into the identity.
ok
An example might be \[\left[\begin{matrix}1 & 0 \\0 & 2\end{matrix}\right]\]
so the second row must be multiplied by a 1/2
http://en.wikipedia.org/wiki/Elementary_matrix
So yes that's right samlam
ya but like I am trying to find the inverse of this
using products of elementary matrices
That's easy to do, just use the usual technique of finding inverse.
How about \[\left[\begin{matrix}1 & 0 \\0 & 1/2\end{matrix}\right]\] ?
If A is an elementary square matrix.
y did we just do that?
ohhhh cuz we are going backwards?
Now write \( A= I_n A \)
Not getting this stuff at all
Then do sequence of row operation on the L.H.S and the prefactor I_n till we obtain \( I_n=BA \) This step will be easy since A is an elementary matrix.
Now we can write \( A^{-1}=B \)
ok so show sth an example plz
I am too tired for a Latex example now :(
LOL Oh u r so annoying
http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-KANPUR/mathematics-2/node27.html That's row-reduction. The only difference between that and what you're talking about with elementary matrices is that when the matrices are elementary its far easier.
ok
That's an nice example Jemurray.
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u have digressed frm d topic

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