Let V be the set of 2 × 2 matrices with determinant 1. For two matrices A and B and any scalar c,
define A (circle plus) B = AB and c (circle times) A = cA. Determine if the set V forms a vector space under this vector addition and scalar multiplication.
Determine if set V froms a vector space under vector addition and scalar multiplication?
I don't think that it does because for 2x2 matrices:
det(cA) = c^2*det(A) which is not equal to 1 (when c is not equal to 1) and so is not in the original space.
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