UPSC NDA Math Model Paper 8

As we know that, any square matrix of order n is said to be idempotent matrix if A2=A.
So, A - 4.
Similarly, as we know that, a square matrix of order n is said to be nilpotent matrix if there exists least positive integer m such that Am=O, where O is the null matrix of order n.
So, B - 1.
Similarly, as we know that, a square matrix of order n is said to be involuntary matrix if A2=I, where I is the identity matrix of order n.
So, C - 2.
As we know that, if A is a real square matrix such that A = A’ then A is said to be a symmetric matrix.
So, D - 3.
Hence, option D is the correct answer