I need help for part c) only

We use the notation In for the identity matrix of size n x n and J\" for the reverser matrix of size n x n. [The reverser matrix is the identity matrix with the column order reversed.) {*1} Verify that the u x 2h reverser matrix J2.\" can be written as In 1'} J2n=Q[ 0 In]QT where Q: I\" I\" ]. 1 E l J... J... Also shovl.r that Q is orthogonal. Let A be a 2n x 27:. matrix with the property that JZnA = AJZH' {13) An example is the 4 x 4 matrix 1 2 3 4 5 E 7 8 S 7" 5 4 3 2 1 Use the factorization of J2\" in part (a) to show that if A satises (13) then the matrix QTAQ is block-diagonal: T _ B U QAQ[ C]. whereBandCarenxnmatriees. The complexityr of solving a general linear equation An: = b of size 2n x 211 is (2f3)(2n)3 = [16)Ir 3M3 . Suppose A has the property dened in part [b]. By how much can the dominant term in the complexity of solving An: = h be reduced if we take advantage of the factorization property],r in part {b}? Explain your