for each condition below, find a pair of square matrices that satisfies it

for each condition below, find a square matrices (and ) that satisfies it

，but

，but

，but , and

let ，find

let ，find

let ，find

let ， find and

let be square matrices with being symmetric, show that is also symmetric

let be symmetric matrices, show that is also symmetric if and only if

let be a square matrix，show that is symmetric

A matrix B is called anti-symmetric if , show that any square matrix can be written as the sum of a symmtric matrix matrix and and an anti-symmetric matrix