If A is 5 by 5, then AB - BA = 0 gives 25 equations for the 25 entries in B. Show that the 25 by 25 matrix is singular by noticing a simple nonzero solution B.

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- Nov 12th 2010, 06:14 PMveronicak5678Singularity
If A is 5 by 5, then AB - BA = 0 gives 25 equations for the 25 entries in B. Show that the 25 by 25 matrix is singular by noticing a simple nonzero solution B.

- Nov 12th 2010, 06:28 PMtopspin1617
I'm not 100% sure exactly what you're trying to ask, but taking $\displaystyle B=I_n$, the $\displaystyle n\times n$ identity matrix, definitely satisfies your equation.

- Nov 12th 2010, 06:57 PMveronicak5678
I'm not exactly sure myself. I get confused by the way the questions in this book are worded. I guess I thought it might make more sense to someone else.

Thanks for answering.