![SOLVED: Question 3) An idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix A is idempotent if and only if AA=A. Show whether the following SOLVED: Question 3) An idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix A is idempotent if and only if AA=A. Show whether the following](https://cdn.numerade.com/ask_previews/1ab2cc82-7f7a-43c7-9dda-97731e37906f_large.jpg)
SOLVED: Question 3) An idempotent matrix is a matrix which, when multiplied by itself, yields itself. That is, the matrix A is idempotent if and only if AA=A. Show whether the following
![SOLVED: 2. Prove that if A and B are idempotent matrices and A B=B A, then A B idempotent. Recall that a square matrix is idempotent when A^2=A, so you know that SOLVED: 2. Prove that if A and B are idempotent matrices and A B=B A, then A B idempotent. Recall that a square matrix is idempotent when A^2=A, so you know that](https://cdn.numerade.com/ask_previews/30c46ca-f1fd-755-fd4b-62bdffbd4a_large.jpg)
SOLVED: 2. Prove that if A and B are idempotent matrices and A B=B A, then A B idempotent. Recall that a square matrix is idempotent when A^2=A, so you know that
![a)idempotent matrixb)involutory matrixc)nilpotent matrix of index 2d)nilpotent matrix of index 3Correct answer is option 'A'. Can you explain this answer? - EduRev JEE Question a)idempotent matrixb)involutory matrixc)nilpotent matrix of index 2d)nilpotent matrix of index 3Correct answer is option 'A'. Can you explain this answer? - EduRev JEE Question](https://edurev.gumlet.io/ApplicationImages/Temp/485050_9478a539-efd2-40c3-80ee-b1ed476b615a_lg.png?w=360&dpr=2.6)