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mateomy
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I was asked this question on a test I just took and I was kinda stumped. I worked it out but I think I did it incorrectly so I was hoping for some input. Thanks.
'A' is a 3x3 matrix and 'I' is the identity matrix for a 3x3. Find the Inverse of 'A' given:
[tex]
(\mathbf{A}\,+\,\mathbf{I})^{2}\,=\,\mathbf{0}
[/tex]
Where '0' is the zero matrix.
So what I did (probably ignorantly) was treat it like any standard algebraic equation; took the radical of both sides, and subtracted the Identity from each side. So I had the zero matrix minus the standard identity 3x3. So I ended up getting a negative identity matrix on the right hand side. So I can see that 'A' equals the negative of an identity matrix. So to find the identity of that I put my 'A' next to and identity to solve in the standard fashion, for the identity of A. Which just happened to be, again, a negative of a 3x3 identity matrix.
Sorry I didn't feel like Latex'ing out all the matrix work but I think it can be followed by what I wrote.
Thanks again.
'A' is a 3x3 matrix and 'I' is the identity matrix for a 3x3. Find the Inverse of 'A' given:
[tex]
(\mathbf{A}\,+\,\mathbf{I})^{2}\,=\,\mathbf{0}
[/tex]
Where '0' is the zero matrix.
So what I did (probably ignorantly) was treat it like any standard algebraic equation; took the radical of both sides, and subtracted the Identity from each side. So I had the zero matrix minus the standard identity 3x3. So I ended up getting a negative identity matrix on the right hand side. So I can see that 'A' equals the negative of an identity matrix. So to find the identity of that I put my 'A' next to and identity to solve in the standard fashion, for the identity of A. Which just happened to be, again, a negative of a 3x3 identity matrix.
Sorry I didn't feel like Latex'ing out all the matrix work but I think it can be followed by what I wrote.
Thanks again.