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Omni-MATH / Does there exist a real 3×3 matrix A such that …andA^2+A^t=I ? (tr (…denotesthetraceofA,A^tisthetransposeofA,andI…

Problem

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problem

Does there exist a real 3×33 \times 3 matrix AA such that \operatorname{tr}(\mathrm{A})=0and and A^{2}+A^{t}=I$ ? (tr $(\mathrm{A})denotesthetraceof denotes the trace of A,, A^{t}isthetransposeof is the transpose of A,and, and I$ is the identity matrix.)
Plain-text mathematical notation (without MathML)
Does there exist a real 3×3 matrix A such that \operatorname{tr}(\mathrm{A})=0andA^{2}+A^{t}=I$ ? (tr $(\mathrm{A})denotesthetraceofA,A^{t}isthetransposeofA,andI$ is the identity matrix.)
Original LaTeX notation
Does there exist a real $3 \times 3$ matrix $A$ such that \operatorname{tr}(\mathrm{A})=0$ and $A^{2}+A^{t}=I$ ? (tr $(\mathrm{A})$ denotes the trace of $A$, $A^{t}$ is the transpose of $A$, and $I$ is the identity matrix.)

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Source and history

task_id
7a0460bb-f042-5932-81cc-76d58b2801d0
task_key
test--7a0460bb-f042-5932-81cc-76d58b2801d0
task_revision_id
1
config / split
/ test

Official source

initial import