Prove that `A+A^T` is symmetric and `A-A^T` is skew symmetric matrix, where `A=[[5,2,-4],[3,-7,2],[4,-5,-3]]`

Prove that A+A^T is symmetric and A-A^T is skew symmetric matrix, where A=[[1,2,4],[3,2,1],[-2,-3,2]]

Express the following matrices as the sum of a symmetric and a skew-symmetric matrix. [[3,3,-1],[-2,-2,1],[-4,-5,2]]

Solve the following:If A is a square matrix,that A-A^T is skew symmentric where A=[[3,5,7],[2,4,-6],[3,8,-5]]

For each of the following matrices,using its transpose,state whether it is a symmetric or a skew-symmetric or neither. [[2,5,1],[-5,4,6],[-1,-6,3]]

For each of the following matrices,using its transpose state whether it is a symmetric,a skew-symmetricor neither. [[1,2,-5],[2,-3,4],[-5,4,9]]

Express the following matrices as the sum of a symmetric and a skew-symmetric matrix. [[4,-2],[3,-5]]

For each of the following matrices,using its transpose state whether it is a symmetric,a skew-symmetric or neither. [[0,1+2i,i-2],[-1-2i,0,-7],[2-i,7,0]]