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Questions › IIT JAM › IIT JAM 2026 › Q27
2 marks, −0.667Mathematics › Matrices, determinants and linear systems › Matrix operations and special matricesHardabout 3 min

IIT JAM 2026 Question 27: Matrices, determinants and linear systems

A 2×22\times22×2 matrix Z=[Z1Z2Z3Z4]Z=\begin{bmatrix}Z_1 & Z_2\\ Z_3 & Z_4\end{bmatrix}Z=[Z1​Z3​​Z2​Z4​​] has the properties: (i) Zi∈RZ_i\in\mathbb{R}Zi​∈R for all iii; (ii) Zi≠0Z_i\neq 0Zi​=0 for some iii; and (iii) Z=Z2=Z3=⋯Z=Z^2=Z^3=\cdotsZ=Z2=Z3=⋯. Which one of the following options is CORRECT?

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A 2×2 matrix Z=[Z₁ Z₂; Z₃ Z₄] has the properties: (i) Zᵢ∈ℝ for all i; (ii) Zᵢ≠ 0 for some i; and (iii) Z=Z²=Z³=⋯. Which one of the following options is CORRECT? (A) Z⁻¹ does not exist for all Z (B) Z^(transpose)≠ Z⁻¹ for all Z (C) Z=Z⁻¹ for some Z (D) For all Z, (h^(transpose)Zh)>0 for all non-zero vectors h with real elements

Also written as: A 2*2 matrix Z=[Z_1 Z_2; Z_3 Z_4] has the properties: (i) Z_i in R for all i; (ii) Z_i!= 0 for some i; and (iii) Z=Z^2=Z^3=.... Which one of the following options is CORRECT?

Matrices, determinants and linear systems has come up 102 times in 7 exams since 2006.

What this question tests

This question is on Matrix operations and special matrices, part of Matrices, determinants and linear systems in Mathematics.

Adding, multiplying and transposing matrices, and the matrices with special properties.

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