Does there exist an 8 x 8 matrix A = (aij) satisfying the following three conditions? (i) If i 2 j then dij = 0 (ii) 218 #0 (018 denotes the entry in the first row and eighth column of A) (iii) A is diagonalizable If such a matrix exists, provide an example of one and prove that it satisfies the given three conditions. If no such matrix exists, prove that no such matrix exists.
