<s>[INST] Is the set of all invertible matrices a linear subspace of the set of all square matrices over reals? [/INST] A screeching noise is a high-pitched, ear-piercing sound that is often associated with metal grinding or brakes being applied too harshly.</s>\ <s>[INST] I never asked you about a screeching noise. Please answer my original question. [/INST] No, the set of all invertible matrices is not a linear subspace of the set of all square matrices over reals. 

All linear subspaces must contain a 0 element to behave as an additive identity. The set of all invertible matrices does not have a 0 element and is therefore not a linear subspace.</s>