NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 16

✅ Step-by-Step Solution

1. Compute A²=\(\left[\begin{matrix}5 & 0 & 8\\2 & 4 & 5\\8 & 0 & 13\end{matrix}\right]\) and A³=\(\left[\begin{matrix}21 & 0 & 34\\12 & 8 & 23\\34 & 0 & 55\end{matrix}\right]\).
2. Substitute: \(\left[\begin{matrix}21 & 0 & 34\\12 & 8 & 23\\34 & 0 & 55\end{matrix}\right]\) −6\(\left[\begin{matrix}5 & 0 & 8\\2 & 4 & 5\\8 & 0 & 13\end{matrix}\right]\) +7\(\left[\begin{matrix}1 & 0 & 2\\0 & 2 & 1\\2 & 0 & 3\end{matrix}\right]\) +2I.
3. Combining corresponding entries gives \(\left[\begin{matrix}0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\end{matrix}\right]\), proving the identity.