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The matrix A={:[(lamda(1)^(2),lamda(1)l...

The matrix `A={:[(lamda_(1)^(2),lamda_(1)lamda_(2),lamda_(1)lamda_(3)),(lamda_(2)lamda_(1),lamda_(2)^(2),lamda_(2)lamda_(3)),(lamda_(3)lamda_(1),lamda_(3)lamda_(2),lamda_(3)^(2))]:}` is idempotent if `lamda_(1)^(2)+lamda_(2)^(2)+lamda_(3)^(2)=k` where `lamda_(1),lamda_(2),lamda_(3)` are non-zero real numbers. Then the value of `(10+k)^(2)` is . . .

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