Let A be an nxn matrix such that A^2+A is invertible, show that A is also invertible.

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[lex]

Note [MATH]\hspace2ex A^2+A=A(A+I)[/MATH]and det(A (A+I)) = det(A) [MATH]\times[/MATH] det(A+I)[MATH] \hspace4ex[/MATH] since both matrices are [MATH]n \times n[/MATH]and a matrix C is not invertible [MATH]\leftrightarrow[/MATH] det(C)=0

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