MathDB

Let

A

and

B

be real

n\times n

matrices. Assume there exist

n+1

different real numbers

t_{1},t_{2},\dots,t_{n+1}

such that the matrices

C_{i}=A+t_{i}B, \,\, i=1,2,\dots,n+1

are nilpotent. Show that both

A

and

B

are nilpotent.

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