NCERT Class 12 · Ch 4 Exercise 4.4 · Q18
NCERT Class 12 Maths · Chapter 4 Determinants · Exercise 4.4 Question 18
If A is an invertible matrix of order 2, find |A⁻¹|.
💡 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: B: 1/|A|.
- From AA⁻¹=I, determinant multiplicativity gives |A|·|A⁻¹|=1.
- Invertibility ensures |A|≠0, so |A⁻¹|=1/|A|.
Master Chapter 4: Determinants
Practise interactive questions, flashcards, visual mind maps, and timed board tests for Determinants.
Related Questions in Determinants
Class 12 Determinants · Mcq Single Correct
If \(\begin{vmatrix}2 & 4\\5 & 1\end{vmatrix}\)=\(\begin{vmatrix}2x & 4\\6 &…
Class 12 Determinants · Mcq Single Correct
The area of the triangle with vertices (−3,0),(3,0),(0,k) is 9 square units. Find k.
Class 12 Determinants · Mcq Single Correct
Let f(x)=\(\begin{vmatrix}0 & x−a & x−b\\x+a & 0 & x−c\\x+b & x+c & 0\end{vmatrix}\). Which…
Class 12 Determinants · Mcq Single Correct
If \(\begin{vmatrix}2 & 3 & 2\\x & x & x\\4 & 9 & 1\end{vmatrix}\)+3=0, find x.
Class 12 Determinants · Mcq Single Correct
If x=−4 is a root of \(\begin{vmatrix}x & 2 & 3\\1 & x & 1\\3 & 2 & x\end{vmatrix}\)=0, find…
Class 12 Determinants · Mcq Single Correct
For a 3×3 real matrix A, det(Aᵀ)=−3. Find det(AAᵀ).