NCERT Class 12 · Ch 4 Exercise 4.4 · Q3
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.4 Question 3
Verify A(adj A)=(adj A)A=|A|I for A=\(\left[\begin{matrix}2 & 3\\-4 & -6\end{matrix}\right]\).
💡 Concept Hints
- Identify whether this needs determinant expansion, an inverse, or the absolute determinant formula for area.
- For a determinant use signed cofactors. For a system first check invertibility; for an area take half the absolute determinant.
✅ Step-by-Step Solution
Final Answer: \(\left[\begin{matrix}0 & 0\\0 & 0\end{matrix}\right]\)
- The cofactor matrix is \(\left[\begin{matrix}-6 & 4\\-3 & 2\end{matrix}\right]\); transpose it to get adj A=\(\left[\begin{matrix}-6 & -3\\4 & 2\end{matrix}\right]\).
- The determinant is \(0\).
- Both products A(adj A) and (adj A)A evaluate to \(\left[\begin{matrix}0 & 0\\0 & 0\end{matrix}\right]\), which is det(A)I.
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