Question

5. A matrix M is called idempotent if M2 = M. Which of the following statements must be true if M is an idempotent matrix? (i) M must be a square matrix. (ii) M must be either the zero matrix, or the identity matrix. (iii) M must be a invertible matrix. (iv) If M is an n xn matrix, then In - M must also be idempotent. (A) Only statements (i) and (ii) are true. (B) Only statements (i) and (iii) are true.; @ All the statements are true.; (D) Only statements (i) and (iv) are true.; ( None of the above;

Answer 1

A matrix is said to be idempotent matrise ..., When milltiplied by itself , it does not changes M2=M.. but this is possible if and only if some Mis a square matrix ** even if it is a Identity matrix**. or Lero matrix they can be I dempotentmatrix since they gield themselves when milltiplied

We know that the Identity matrix minus Idempotent matrix is also a idempotent matoid from the properties of Idempotent matriz .

A matxit to be a Idempotent matrict must be a Squeave matrit and it must be invertible :: All statements are true option C is correct