Q86.The total number of 3 × 3 matrices A having enteries from the set (0, 1, 2, 3) such that the sum of all the diagonal entries of AAT is 9, is equal to
What This Question Tests
This question tests the understanding of determinant properties, particularly similarity transformations, and the ability to compute determinants of matrices containing complex cube roots of unity, simplifying the process through algebraic manipulation.
Concepts Tested
Formulas Used
det(P⁻¹AP) = det(A)
det(B²) = (det(B))²
1 + ω + ω² = 0
Determinant formula for 3x3 matrix
📚 NCERT Sections This Tests
5.15 — Discuss The Nature Of Bonding In The Following Coordination Entities On The
Chemistry Class 11 · Chapter 5
5.15 Discuss the nature of bonding in the following coordination entities on the basis of valence bond theory: (i) [Fe(CN)6] 4– (ii) [FeF6] 3– (iii) [Co(C2O4)3]3– (iv) [CoF6] 3–
8.17 — Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products
Chemistry Class 12 · Chapter 8
8.17 Complete each synthesis by giving missing starting material, reagent or products
5.12 — Write All The Geometrical Isomers Of [Pt(Nh3)(Br)(Cl)(Py)] And How Many Of
Chemistry Class 11 · Chapter 5
5.12 Write all the geometrical isomers of [Pt(NH3)(Br)(Cl)(py)] and how many of these will exhibit optical isomers?
📋 Question Details
- Chapter
- Matrices & Determinants
- Topic
- Determinant properties, complex cube roots of unity
- Year
- 2021
- Shift
- 16 Mar Shift 1
- Q Number
- Q86
- Type
- Numerical
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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