This week this exclusive club, based at the glorious East Lothian links, hosts the world's best female players as they compete in the AIG Women's Open.

Until 2017, Muirfield was a men-only golfing enclave and the club's initial failure to find the two-thirds majority required to alter its constitution and allow women members had seen it it struck from the men's Open rota.

The loss of this status concentrated minds and a second ballot proved more progressive, allowing women to join for the first time. Muirfield is still waiting to be assigned a 17th men's Open, having last held one in 2013, but it is back on the list of candidate courses.

And, although it is not the traditional Claret Jug at stake, arguably the fairest links test in Scotland is staging big-time golf again.

On Thursday morning, Scotland's Matthew will strike the first tee shot in the final women's major of the year and no doubt the 2009 champion's mind will wander back to her first Muirfield visits.

They involved voluntarily picking litter and carrying the scoreboard at the 1992 championship.

"I do remember it was horrific weather one of the times I was scoring," Matthew recalled. "I was actually fortunate enough to be in John Cook's group the last day when [Sir Nick] Faldo won and John Cook, I think, missed that little putt on 17."

Muirfield has been staging Opens since 1892 but, by joining venues such as Royal Lytham, Carnoustie, St Andrews Old Course, Royal Birkdale and Turnberry, it is also now a venue for one of the world's biggest female tournaments.

"I think it's great to come here," Matthew added. "Obviously over the last probably 10 years, we started going to all The Open venues that, over the last 50, 60 years, you've seen the men playing in.

"And I think that just elevates this championship - and we are now going to courses that people are used to seeing. I think it's good for us."

Matthew, a native of nearby North Berwick, added: "For me personally, obviously living and growing up along the road, I never would have imagined ever playing a major so close to home."

At Carnoustie last year, the 52-year-old watched with delight as Sweden's Anna Nordqvist completed a stirring victory that helped stoke confidence in Matthew's team for a successful Solheim Cup defence later that summer.

Now the Swede is soaking up the atmosphere before trying to retain her title this week. "I've heard a lot about Muirfield," said Nordqvist, 35.

"I know the guys have played here over the years, so I think it's an amazing opportunity for us to have Muirfield added to our Open rotation.

"It's pretty cool seeing the pictures. I've been looking forward to this week for a long time."

Leading contenders are unanimous in their delight that Muirfield is staging the tournament. "I was extremely excited to come out and play this event this year," said Olympic champion Nelly Korda.

"I knew the history, and the fact that we were going to be the first female tournament out here, too, was pretty amazing.

"So I was more excited to actually be out here and to get to play this golf course and soak it all up, as well as the history of this place."

American Korda has made strong progress since returning from a blood clot in her arm which cost her a place in the year's opening major, the Chevron in March. The 24-year-old has subsequently posted two major top 10s, including a share of eighth at the recent Evian Championship.

That event was won by the resurgent Canadian Brooke Henderson, another top star keen to highlight this week's historic significance. "To be playing this year, it really means a lot to all of us," said the 24-year-old world number five.

"It's just proof that the women's game is continuing to grow, the purse sizes are increasing, we're on network TV more and we're playing these better venues.

"It's just a really fun time to be a part of women's golf because it is growing so much and we feel like we're making a difference for future generations."

And those youngsters volunteering this week, taking maybe a first chance to walk the hallowed turf of Muirfield, can do so confident that if they can achieve a high enough standard, nothing will stop them from competing for the biggest prizes there in the future.