alleryA square matrix $A$ is called **idempotent** if:
A$A^2 = I$
B$A^2 = A$
C$A^2 = 0$
D$A^T = A^{-1}$
Answer & Solution
Correct answer: B. $A^2 = A$
**Idempotent:** $A^2 = A$.
The identity matrix and the zero matrix are trivial examples.
Projection matrices in linear algebra are non-trivial examples.
Option A defines an involution (e.g. reflection)
option C defines a nilpotent of index 2
option D defines an orthogonal matrix.
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