Consider the transposition linear map T:Mn×n​(R)→Mn×n​(R) given by T([mij​])=[mji​]. 1. Show that λ=±1 are the only eigenvalues of T. 2. Previously, on Homework \#5, we met the eigenspaces of E+1​ and E−1​ of transposition. What did we call them on that homework? 3. Find a basis α of M2×2​(R) such that [T]αα​ is a diagonal matrix.