Which of the following functions T are linear transformation

Which of the following functions T are linear transformations? T: M n Times n(R) rightarrow M n Times n defined by T(A) = the reduced echelon form of A T: M n Times n(R) rightarrow M n Times n (R) defined by T(A) = P^-1AP where P M n Times n is fixed, invertible matrix.

Solution

The answer is option A as we use the reduced echelon form of A in Linear transformations.