Mathematics · Linear Algebra

Let M2(ℝ) be the vector space of all 2×2 matrices over ℝ. Consider the linear transformation T: M2(ℝ) → M2(ℝ) defined by T(X) = AXB, where: A = [ 1 -2 ; 1 4 ] and B = [ 6 5 ; -2 -1 ]. If P is the matrix representation of T with respect to the standard basis of M2(ℝ), then which of the following statements is TRUE?