Appeared in: 2026 (3 sets)
For a square matrix $A$, $(3A)^{-1} =$
(A) $3A^{-1}$
(B) $9A^{-1}$
(C) $\frac{1}{3}A^{-1}$
(D) $\frac{1}{9}A^{-1}$
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Official Evaluation Steps & EL10 Insight
Step 1 (Formula / Governing Law): [1/2 Mark]
According to the properties of the inverse of a matrix, for any non-zero scalar $k$ and an invertible square matrix $A$, the following property holds:
$$ (kA)^{-1} = \frac{1}{k} A^{-1} $$This is derived from the definition of an inverse, where $(kA) \cdot (\frac{1}{k