If A is a $3 \times 3$ invertible matrix, show that for any scalar $k \neq 0$, $(kA)^{-1} = \frac{1}{k} A^{-1}$. Hence calculate $(3A)^{-1}$, where $A = \begin{bmatrix} 2 & -1 & 1 \\ -1 & 2 & -1 \\ 1 & -1 & 2 \end{bmatrix}$.

Year	Paper Code	Set	Position
CBSE 2025	Series 65-4	Set 1	Question 32
CBSE 2025	Series 65-4	Set 2	Question 33
CBSE 2025	Series 65-4	Set 3	Question 35

• Step 1: Stating the fundamental formula / law statement (+1 Mark)
• Step 2: Intermediate mathematical substitution or proof steps (+1 Mark)
• Step 3: Correct final value or conclusion with mandatory SI units (+1 Mark)