MathDB

Let

A

be an

n\times n

matrix of real numbers for some

n\ge 1.

For each positive integer

k,

let

A^{[k]}

be the matrix obtained by raising each entry to the

k

th power. Show that if

A^k=A^{[k]}

for

k=1,2,\cdots,n+1,

then

A^k=A^{[k]}

for all

k\ge 1.

Problem Statement