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Linear Algebra

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Moderate

When is a Square Matrix Unit Idempotent?

LINALG-ECCMVX

Let $E$ be a square matrix with all but one entry equal to $0$. Suppose the nonzero entry is $b$ and that it is found in row $i$, column $j$.

In which of the following cases will $E$ be an idempotent matrix?

A

$i=j$ and $b=1$

B

$i=j$ and $b=-1$

C

$i=j$ and $b=2$

D

$i\neq j$ and $b=1$

E

$i\neq j$ and $b=-1$

F

$i\neq j$ and $b=2$