NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.4 Question 12

✅ Step-by-Step Solution

1. The determinants are \(1\) and \(-2\), both nonzero.
2. Compute A⁻¹=\(\left[\begin{matrix}5 & -7\\-2 & 3\end{matrix}\right]\) and B⁻¹=\(\left[\begin{matrix}- \frac{9}{2} & 4\\\frac{7}{2} & -3\end{matrix}\right]\).
3. Their reversed product B⁻¹A⁻¹=\(\left[\begin{matrix}- \frac{61}{2} & \frac{87}{2}\\\frac{47}{2} & - \frac{67}{2}\end{matrix}\right]\).
4. Directly AB=\(\left[\begin{matrix}67 & 87\\47 & 61\end{matrix}\right]\) and (AB)⁻¹=\(\left[\begin{matrix}- \frac{61}{2} & \frac{87}{2}\\\frac{47}{2} & - \frac{67}{2}\end{matrix}\right]\), the same matrix.