Whether male and female Siamese fighting fish can live together depends on factors such as the breed of the fighting fish, the size of the fish tank, and whether they are in the breeding period.

Whether Different Breeds of Siamese Fighting Fish Can Live Together
Chinese Siamese Fighting Fish: Chinese Siamese fighting fish have a relatively mild temperament. A male and a female can be kept together. Even if they chase each other, they usually won't cause serious harm. If the fish tank is large enough and there are sufficient shelters provided, you can try keeping them together. However, you still need to closely observe their behavior to prevent attacks and injuries.
Siamese Fighting Fish (Betta splendens): Siamese fighting fish are more aggressive. Even for a male and a female, except during the breeding period, the male Siamese fighting fish will attack the female, which is likely to injure the female. Therefore, it is generally not recommended to keep Siamese fighting fish together, unless it is during the breeding period.
Precautions for Mixed Breeding
Size of the Fish Tank: Ensure that the fish tank is large enough and provide sufficient shelters, such as aquatic plants, stones, etc., to reduce fighting and injuries.
Water Quality and Temperature: Maintaining stable water quality and a suitable water temperature (24-27°C) is an important condition for maintaining the health of Siamese fighting fish.
Observe Behavior: Closely observe the behavior of the Siamese fighting fish. Once any attacking behavior is found, they should be separated for breeding in a timely manner to avoid injuries.