Discussion
Match the matrix property with its defining relation.
1. Symmetric 2. Orthogonal 3. Idempotent
P. Its square equals itself Q. It equals its own transpose R. Its transpose is its inverse
Answer: D
Each relation constrains the eigenvalues in a characteristic way, real for symmetric, of unit modulus for orthogonal, and zero or one for idempotent. Recognising the form is usually quicker than computing the spectrum directly.
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