Question

For any square matrix A, prove that A+A1 is symmetric matrix and A-A1 is skew symmetric matrix​

Answer 1

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Step-by-step explanation:

ANSWER ::

Let B = A + A '

NOW

B' = ( A + A ')' = A' + ( A') ' = A' + A = A + A ' = B

SO B = A + A ' is symmetric matrix

Let P = A - A '

P' = ( A - A ')' = A' - ( A') ' = A' - A = - (A - A ') = - P

SO P = A - A ' is skew symmetric matrix