Yes, the set of all invertible matrices is a linear subspace of the set of all square matrices over the real numbers.

A subspace is a subset of a vector space that is itself a vector space, meaning that it must contain the zero vector and be closed under addition and scalar multiplication. The set of all invertible matrices is a subset of the set of all square matrices, and it is closed under addition and scalar multiplication because if two matrices are invertible, then their sum and scalar multiple are also invertible.

So, the set of all invertible matrices is a linear subspace of the set of all square matrices over the real numbers.
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