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Matrices and Determinants Part 3

Section: Mathematics

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Question : 22

Total: 100

Let R=(

x	0	0
0	y	0
0	0	z

) be a non-zero 3×3 matrix, where xsin‌θ=ysin‌(θ+‌

)=zsin‌(θ+‌

) ≠0,θ∈(0,2π). For a square matrix M, let trace (M) denote the sum of all the diagonal entries of M. Then, among the statements:
(I) Trace (R)=0
(II) If trace(adj(adj(R))=0, then R has exactly one non-zero entry.

[30-Jan-2024 Shift 2]

Both (I) and (II) are true
Neither (I) nor (II) is true
Only (II) is true
Only (I) is true

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