If $A$ is a symmetric matrix, then $A^2$ is also symmetric

Why not directly?: We're given $\;A\;$ is symmetric $\;\iff A^t=A\;$ , and then

$$(A^2)^t=(AA)^t=A^tA^t=AA=A^2\implies A^2\;\;\text{is symmetric}$$

Or in short: $\;(A^2)^t=(A^t)^2=A^2\;$

Tags:

Linear Algebra

Abstract Algebra

Matrices

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