Define a map ? : M2 ? {1} ta??r^k ? (?1)^k. Prove ? is a well-defined homomorphism. (Remark: This provides an algebraic way to define the orientation of an isometry. Those corresponding to +1 are called orientation preserving, and those corresponding to ?1 are called orientation reversing.)

Define a map V : M2 ->{+1} tapork > (-1) k Prove I is a well-defined homomorphism. Remark: This provides an algebraic way to define the orientation of an isom- etry. Those corresponding to +1 are called orientation preserving, and those corresponding to -1 are called orientation reversing. )