Answer

Solution

1. 1

   $Ax=x$ for all $x\in\mathbb{R}^{3}$ means $(A-I)x=0$ for every $x$, which forces $A=I$, the $3\times 3$ identity matrix. The identity matrix is neither the all-ones matrix in (B) nor the anti-diagonal permutation matrix in (C). Therefore the unique $A$ is the identity, which is none of the explicit matrices listed.

Answer structure / marking notes

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