Question
(a) Is the set of $n \times n$ matrices with $\operatorname{det} A=1$ a subspace of $\mathcal{M}_{n \times n}$ ?(b) What about the matrices with $\operatorname{det} A=0$ ?
Step 1
A subset \( W \) of a vector space \( V \) is a subspace if and only if it satisfies three conditions: (1) it contains the zero vector of \( V \), (2) it is closed under vector addition, and (3) it is closed under scalar multiplication. Show more…
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