Can someone on a gluten free diet eat cornflour?

My grandma is intolerant to dairy and gluten. She's coming round tomorrow and I'm baking her a cake. It's a fat-free sponge, so the dairy doesn't matter. It's got 50g flour, but I'm using gluten free, a teaspoon of baking powder, again I'm using gluten free, but it also has 50g cornflour. I don't know whether someone on a gluten free diet can eat it or not. My mum reckons it's fine, but I'm slightly cautious. So can she eat my cake, or will she be ok if it's only that amount? Or will I have to eat the cake myself, and make her a meringue or something?