Suppose, M is a lower triangular matrix with all diagonal entries zero. The resultant matrix of M+I will be ___________(a) idempotent(b) singular(c) nilpotent(d) inverseI have been asked this question in final exam.My doubt is from Permutation Groups topic in section Groups of Discrete Mathematics

Suppose, M is a lower triangular matrix with all diagonal entries zero

1.	Suppose, M is a lower triangular matrix with all diagonal entries zero. The resultant matrix of M+I will be ___________(a) idempotent(b) singular(c) nilpotent(d) inverseI have been asked this question in final exam.My doubt is from Permutation Groups topic in section Groups of Discrete Mathematics
Answer» Correct ANSWER is (b) singular Best explanation: SINCE, M is a lower triangular matrix with diagonal ELEMENTS zero, then we add I and it will RESULT in a lower triangular matrix with all diagonal entries 1. Thus, all EIGENVALUES M+I are non zero (eigenvalues of triangular matrix is the diagonal elements). So, determinant will never be zero. Hence, the matrix can have inverse property.

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