Prove that the method of moments estimators of the mean and variance of a normal distribution are

Question:

Prove that the method of moments estimators of the mean and variance of a normal are also the M.L.E.’s.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...