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Is the identity matrix a projection matrix, and if so, is it the only projection matrix which is invertible? Also when considering $2\times 2$ matrices which satisfy $A^2=A^T$ what satisfies this? How can it be proven that projection matrices fit under this umbrella as well as the identity matrix, as well as the zero matrix.

Ittay Weiss
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user64156
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  • I added the correct latex codes to correctly format your question. You might wish to have a look at your question now so you learn hot to type it correctly yourself. – Ittay Weiss Feb 27 '13 at 04:21

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$A$ a projection means $A^2=A$, so for $A=I$, since $A^2=I=A$, indeed $I$ is a projection. Further, if $A$ is an invertible projection, then $A^2=A$, so multiplying by the inverse $A^{-1}$ we get that $A=I$. So, yes, the only invertible projection is $I$. I'm not quite sure what are you asking in the rest of your question.

Ittay Weiss
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