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If [tex]A^2 = 0[/tex], show that [tex]I - A[/tex] is invertible.
So we know that [tex]\det(A^2) = (\det A)^2 = \det 0 \Leftrightarrow \det A = 0[/tex]
We should now show that [tex]\det(I-A) \not= 0[/tex].
But I'm not sure how to do that. Could someone kick me in the right directon?
So we know that [tex]\det(A^2) = (\det A)^2 = \det 0 \Leftrightarrow \det A = 0[/tex]
We should now show that [tex]\det(I-A) \not= 0[/tex].
But I'm not sure how to do that. Could someone kick me in the right directon?