NCERT Class 12 · Ch 4 Miscellaneous Exercise · Q8
NCERT Class 12 Maths · Chapter 4 Determinants · Miscellaneous Exercise Question 8
For A=diag(x,y,z), where xyz≠0, 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: A: diag(1/x,1/y,1/z).
- A diagonal matrix is invertible when each diagonal entry is nonzero.
- Multiplying diag(x,y,z) by diag(1/x,1/y,1/z) in either order gives I₃.
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