Does there exist an 8 x 8 matrix A - (a) satisfying the following three conditions? (1) If i 2j then ay -0 (Hi) as 0 (as denotes the entry in the first row and eighth column of A) (ii) A is dingonalizable 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.

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