ID: Class: 12 Subject: Math Topic: Matrices and Determinants Type: Long (LA) Year: 2025

Question:

If A is a \(3\times3\) invertible matrix, show that for any scalar \(k\ne0.\), \((kA)^{-1}=\frac{1}{k}A^{-1}.\) Hence calculate \((3A)^{-1}\) where \(A=\begin{bmatrix}2&-1&1\\ -1&2&-1\\ 1&-1&2\end{bmatrix}.\)