Please explain questions 33, 34, 35, 36, 37 and also give their correct options

1.33. Let A be a nipolent 2 x2 square matrix of index 10. Then ) A = 0 (ii) rank A=l (ii) A2 = 0 (iv) rank A =2 1.34. If A, B, C are three n x n non-singular A matrices, then rank of c/is i) atleast rank A + rank C i) rank A + rank B + rank C ii) rank A + rank C (iv) rank A 1.35. The rank of the real matrix 3 A= 3 3 3is 3 3 )1 i) 2 ii) 3 (iv) 0 1.36. For an m x n matrix A with m S n, we always have ) rank A sm (i) mS rank A Sn (ii) n S rank A (iv) m S rank A Sm+n f (5 0 o 1.37. Let A = |1 5 0 . Then for which X o1 5 there exists a scalar 2 such tha AX AX. 0x