The dam was sorely needed to provide power for the area, but to get that, a lot of people were displaced and their homes covered with water behind the dam. This was the tradeoff. Some might say that it was not really an equal, or balanced tradeoff, and others would say it was.
An idempotent matrix is a matrix which gives the same matrix if we multiply with the same. in simple words,square of the matrix is equal to the same matrix. if M is our matrix,then MM=M. then M is a idempotent matrix.