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Let S be the set which contains all poss...

Let S be the set which contains all possible values of `l, m, n, p, q, r` for which
`A=[(l^(2)-3,p,0),(0,m^(2)-8,q),(r,0,n^(2)-15)]` be a nonsingular idempotent matrix. Then the sum of all the elements of the set S is __________ .

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