How is B correct. Unless we fix the size of a nonsingular matrix to say n*n only then will the multiplication operator be closed. For a set of all non singular matrices, multiplication operator will not be even defined for some pairs.

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.