1)Find 2 bases a=(v1,v2,v3) and b=(w1,w2,w3) of R3 such that both of them are non standard and yet the matrix of the identity map I:R3--R3 is the identity map

2)Let U be a 4 dimensional vector space over R and suppose that U=V+W, where dim v=dim W=2. Further, assume that {v1,v2,w1,w2} is a basis of U, where {v1,v2} is a basis of V and {w1,w2} is a bsis of W. Let T:U--U be a linear operator such that
i) T sends every vector in V to a vector in V and every vector in W to a vector in W;
ii)T sends every vector in V to a vector in W and every vector in W to a vector in V;
What can you say

Question

1)Find 2 bases a=(v1,v2,v3) and b=(w1,w2,w3) of R3 such that both of them are non standard and yet the matrix of the identity map I:R3-->R3 is the identity map

2)Let U be a 4 dimensional vector space over R and suppose that U=V+W, where dim v=dim W=2. Further, assume that {v1,v2,w1,w2} is a basis of U, where {v1,v2} is a basis of V and {w1,w2} is a bsis of W. Let T:U-->U be a linear operator such that 
i) T sends every vector in V to a vector in V and every vector in W to a vector in W;
ii)T sends every vector in V to a vector in W and every vector in W to a vector in V;
What can you say