I'm preparing for an end of year linear algebra test which briefly covers things about subsets of Matnxn and their relations to subspaces of Matnxn; I found the following question: Which of the following subsets of Matn×n are subspaces of Matn×n? (i) Symmetric matrices (i.e. matrices A such that AT = A). (ii) Skew-symmetric matrices (i.e. matrices A such that AT = −A). (iii) Orthogonal matrices (i.e. matrices A such that AT = A−1). (iv) Singular matrices. (v) Invertible matrices. (vi) Echelon matrices. (vii) Reduced echelon matrices. ---- I'd appreciate some guidance on how to tell which of the above apply.. is it the same as showing that vectors in a subset are subspaces when they're closed under addition and linear multiplication? thanks.