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One more abstract algebra question. A matrix U is called skew-symmetric if U = U^t.

One more abstract algebra question.

A matrix U is called skew-symmetric if U = −U^t. Show that every realsquare matrix A can be written uniquely in the form A = S + U where S issymmetric and U is skew-symmetric

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Ans :−¿
T Let U be the skew−symmetric ¿ isU =−U ∧let us supposethat A be any
real ¿ Then we have ¿ show that A=S+U , Where S is symmetric ¿is S=S T
¿ the expressionis alsounique
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