Let a square matrix of order n satisfy a ^ 3 = 0, then the invertible matrix in the following matrices B = A-E, C = a + e, d = a ^ 2-A, f = a ^ 2 + A is, and it is proved that Such as the title

Proof: A & sup3; - E = - e
I.e. (A-E) (A & sup2; + A + e) = - e
So, (A-E) ^ (- 1) = - (A & sup2; + A + e) B is reversible
A & sup3; + e = E has
(A+E)(A²-A+E)=E
So, (a + e) ^ (- 1) = (A & sup2; - A + e) C is reversible

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