Amatrix is skew symmetric of a^t = -a. prove that if b is a square matrix that 1/2(b - b^t) is skew symmetric and 1/2(b + b^t) is symmetric. find the inverse of a = [1 2 0 2 1 0 0 0 3] if it exists. a) give a 2 times 2 example that proves that the sum of two invertible matrices need not be invertible. b) give a 2 times 2 example that proves that the sum of two singular matrices need not be singular. let a be an invertible matrix. prove that if ab is defined then rank ab = rank b and if ba is defined that rank ba = rank b.