Group list by last 2 months and count its distinct items

Question

Hi to all. Good day. I want to group a list by last 2 months and count how many products are their in every month and also count distinct category for every product sold in each month

I have a list. It contains a class named ProductTransaction.

 

List<ProductTransaction> productList = new List<ProductTransaction>();
class ProductTransaction
{
string product;
DateTime date_sold;
string  category;
} 
productList.Add(new ProductTransaction () {product="sword", date_sold=03/05/2017,category="weapons"});
productList.Add(new ProductTransaction() {product="sword2", date_sold=03/01/2017,category="weapons"});
productList.Add(new ProductTransaction() {product="potion", date_sold=02/05/2017,category="life"});
productList.Add(new ProductTransaction() {product="jacket", date_sold=02/03/2017,category="clothing"});
productList.Add(new ProductTransaction() {product="jacketofBear", date_sold=02/01/2017,category="clothing"});
 

I want to achieve a data like below.Please see attached image file

Month          productCount     categoryCount

March                2                           1
February           3                           2


Thank you and GodBless