## Acalytica

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Identify which of the following collections of matrices form a linear subspace in the linear space $\operatorname{Mat}_{2 \times 2}(\mathbb{R})$ of all $2 \times 2$ real matrices?

a) All invertible matrices.
b) All matrices that satisfy $A^{2}=0$.
c) All anti-symmetric matrices, that is, $A^{T}=-A$.
d) Let $B$ be a fixed matrix and $\mathcal{B}$ the set of matrices with the property that $A^{T} B=$ $B A^{T}$.
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