PLEASE HELP SOON AND TRY TO EXPLAIN. Prove that if a, b, c, d are non zero real numbers, not all equal, and if a+1/b=b+1/c=c+1/d=d+1/a then |abcd|=1. Thx!

To diagonalize an nxn matrix a means to find an invertible matrix p and a diagonal matrix d such that a pdp d p ap or [1 3 dh epap 3 let a=-3 -5 -3 3 3 1 step 1: find the eigenvalues of matrix a "2's" step 2: find the corresponding eigenvectors of a step 3: createp from eigenvectors in step 2 step 4 create d with matching eigenvalues.