we know under binary operation *
1.Groupoid→ closed
2.Semi group ->Associative
3.Monoide->Identity should present
4.Group->Inverse should present
5.Abelian group→ commutative
For remind this order i use (Ground se mat Gharjao app)
matrix “A” is non singular then $_{A}-1$ will present
For make a matrix a group we need to give guarantee that inverse is present but for every type of matrix we can’t give guarantee but only for non singular.