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## Homework Statement

Given a matrix B, if B = B

^{2}, is (B+I) invertible?

**2. The attempt at a solution**

det(B) = 0 or 1

rref(rref(B) + I) is I, so (rref(B) + I) is invertible

if det(B) = 1:

let E

_{1}E

_{2}...E

_{n}= B

then E

_{1}E

_{2}...E

_{n}(rref(B) + I) = B + E

_{1}E

_{2}...E

_{n}

I'm not sure if what I did is even useful =(