I need help about those matrix problems, thank you so much!

Problem 11. Show that the determinant of an orthogonal matrix i5 +1 or 1, Problem 12. Show that the Pauli spin mat-rim om Hormitlon and thereforo Unitary 115ng your results from problem 5. Prohlam 5. The Pauli spin matrlmt in quantum mmhnnlcs um _ I] 1 _ a t _ 1 n \"a" 1 a \"H' l n a\" n l Show that a: = a: = of = l where I'. is the identity matrix. Also Show that any pair nl' them matrices antlmmmuta, that 15, mo} now: Where i.j = {smut} and 1' 7'5 5}. Elm that tht:r matriuea satisfy the outnmutution relation 6,615 aka, = Slim. Problem 6. The following matrix pmdunt is tum-d in dlamtaalng two thin lansm in air: \"=0: 4%) ( 3*) (a t") what: I. and h are the focal langths ml the 1mm and at 1E the dltane between tlmm. Find M and (let M . What it the physical meaning of the elmtrent M12? Problem 1". Elven 1hr: matricea l ---l 1 l [I 1 -'.I. 2 2 l. 2 Find A'H H", 5"}213 and B"A"'I.ti. Show that the last two matrlm are humus of each other. Problem a. The previous problem in a. Spatial nan of a general theorem for ill'lmrlli at the product of two matrices. Pram that [A3]\" = H411\". Problem 9. Givm the matrix 1 [I ll 11 = +2l El [1' 1 I. -+- l [l nd the trmpm, the inverse, the complex conjugate. tutti tlm lit-.Imjtinn conjugatn ol' A. Verify that rid\" = 1431 = l Problem to. Show that the matrix of it rotation about the t-mit is orthogonal