prove these 2 questions using the LaTex with the dollar signs to for my Rmardown document

Question 1 Prove Result 4.1 - there are two parts to this - the last is to show \\(\\Sigma*{-1}\\) is positive definite! Make sure you say what positive definite means! Result 4.1. If is positive definite, so that 7 exists, then Xe = Ae implies Xe = (+)e so (A, e) is an eigenvalue-eigenvector pair for { corresponding to the pair (1/A, e) for "1. Also, 7! is positive definite. Question 2 Prove Result 4.7 - please note there are two parts! Show your working under sub-sections a) and b) Result 4.7. Let X be distributed as N,(#, ) with |2| 0. Then (a) (X w)'= "(XK pz) is distributed as x2, where x, denotes the chi-square distribution with p degrees of freedom. (b) The N,(#,%) distribution assigns probability 1 a to the solid ellipsoid {x: (x p)'X1(x p) = x2(a)}, where x%(@) denotes the upper (100a)th percentile of the x4 distribution