Please solve all the following eigen quantum physics problems (questions in picture) asap. Show all your work clearly, show all your work, and formulas used. Thanks!

An operator A, representing observable A, has two (normalized) eigenstates a1) and a2), with eigenvalues a1 and a2, respectively. Operator B, representing observable B, has two (normalized) eigenstates (b1) and 162), with eigenvalues b1 and b2, respectively. The eigenstates are related by la1) = Oil CO 162) , 1a2 ) = 161) CTI CO 162) . (1) Suppose () is a state such that, when measuring A, the probability of getting an is 3/4. For the same state (), what is the probability of getting bi and b2 when measuring B? With the given information, is this probability uniquely determined? Find the matrix elements (p| P [p') in two ways: (a) Using the fact that [p), by definition, is the eigenstate of P. (b) With (xp) = eipx/h and (x| Place') = -ihd'(x - x'), perform a change of basis from the position space to the momentum space