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Prove that for any square matrix A , A+AT is symmetric & A-AT is skew symmetric matrix.

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Any square matrix can be written as sum of Symmetric and Skew Symmetric matrix and that too UNIQUELY

(a) Show that the matrix A=[[ 4/5 0 -3/5; -9/25… ]

Prove that if A is an Invertible Matrix then AB = AC Implies B = C