Solution to Simple Matrix Equation

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SUMMARY

The discussion clarifies that a matrix squared equaling the original matrix does not limit the original matrix to only the zero matrix or the identity matrix. It establishes that any diagonal matrix containing ones and zeros along its diagonal will also satisfy this condition. This expands the understanding of matrix properties beyond the commonly assumed cases.

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lapo3399
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If a matrix squared is equal to the original matrix, does that mean that the original matrix had to be either the zero matrix or the identity matrix?

Thanks.
 
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Not necessarily. Any diagonal matrix with ones and zeros along the diagonal will have this property.
 

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