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If X is an idempotent nonsingular matrix, then X must be ___________(a) singular matrix(b) identity matrix(c) idempotent matrix(d) nonsingular matrixThe question was posed to me during an internship interview.My question is based upon Groups topic in chapter Groups of Discrete Mathematics

Answer»

Correct OPTION is (b) IDENTITY matrix

To explain: Since X is idempotent, we have X^2=X. As X is NONSINGULAR, it is invertible. THUS, the INVERSE matrix X^-1 exists. Then we have, I=X^-1X = X^-1X2=IX=X.



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