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let a be a 2 by 2 real matrix with determinant of a is equal to 1 and trace of a is equal to 3 what is the value of trace of a square for options given to us and we have to find right one option what need to find we need to find trace of a square that is if lambda 1 plus lambda 2 are eigen values of a square then we have to find their sum if lambda 1 and lambda 2 are eigen values of a square remember one point to solve this problem if lambda i is eigen value of is eigen value of a matrix a then lambda i raised to the power n will be eigen value of a raised to the power n use this concept and try to solve this problem as determinant of a determinant of a is given to us and equal to 1 also trace of a is equal to 3 and we have to find trace of a square we have to find trace of a square determinant of a is equal to 1 if lambda 1 and lambda 2 are eigen value eigen value of a then lambda 1 into lambda 2 product determinant can be written as in terms of eigen values by product is equal to 1