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Linear Algebra

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Inverse Square Matrices

LINALG-7AYNEJ

All but one of the following conditions are equivalent to the $n\times n$ matrix $A$ being invertible.

Which one ISN'T?

A

The column vectors of $A$ span $\mathbb{R}^n$

B

The row vectors of $A$ span $\mathbb{R}^n$

C

$A^T$ is invertible

D

$A^2=A$

E

$A-I_n$ is nilpotent