NCERT Class 12 Maths · Chapter 3 Matrices · Exercise 3.2 Question 1

✅ Step-by-Step Solution

1. Addition and subtraction are entrywise; scalar multiplication multiplies every entry.
2. A+B = \(\left[\begin{matrix}3 & 7\\1 & 7\end{matrix}\right]\).
3. A−B = \(\left[\begin{matrix}1 & 1\\5 & -3\end{matrix}\right]\).
4. 3A−C = \(\left[\begin{matrix}8 & 7\\6 & 2\end{matrix}\right]\).
5. For AB, the inner dimensions agree: 2. Its order is 2×2. Use cᵢⱼ=Σₖaᵢₖbₖⱼ.
6. Row 1: \(c_{11}=(2)(1) + (4)(-2)=-6,\quad c_{12}=(2)(3) + (4)(5)=26\).
7. Row 2: \(c_{21}=(3)(1) + (2)(-2)=-1,\quad c_{22}=(3)(3) + (2)(5)=19\).
8. AB = \(\left[\begin{matrix}-6 & 26\\-1 & 19\end{matrix}\right]\).
9. For BA, the inner dimensions agree: 2. Its order is 2×2. Use cᵢⱼ=Σₖaᵢₖbₖⱼ.
10. Row 1: \(c_{11}=(1)(2) + (3)(3)=11,\quad c_{12}=(1)(4) + (3)(2)=10\).
11. Row 2: \(c_{21}=(-2)(2) + (5)(3)=11,\quad c_{22}=(-2)(4) + (5)(2)=2\).
12. BA = \(\left[\begin{matrix}11 & 10\\11 & 2\end{matrix}\right]\).