How smart can an Egyptian Mau be?

My best friend has an Egyptian Mau and she is so so so smart. I don't know if this is strange for a cat but her cat takes showers with her and when she asks for the shampoo or conditioner bottle she knows what it is and gets it for her. When she asks for her brush shell specifically get her brush and when she asks for the cats brush shell go and get it. Shell follow her and her dog to her school sometimes and sometimes goes with her dog to pick her up from school. When she tells her its bedtime and to go to sleep shell go jump right on her bed next to her dog and sleep and helps her dog wake her up in the morning. Shes even like her mother and make sure she eats breakfast in the morning and pats pieces of fur off her jeans. Like her dog she knows exactly what time shes supposed to be to sleep and helps her dog tuck her in at night to. Can cats really be this smart?