M is a 2-square matrix of rank 1, then M is (a) diagonalizable and non-singular (b) diagonalizable and nilpotent (c) neither diagonalizable nor nilpotent (d) either diagonalizable or nilpotent

Question

explain plz .... ans given (d)

Answer 1

matrix can be in form of      a     b          (or)     a     0    (or)     0  a

                                         0     0                    0     0              0  0

in first and 2nd case matrix is diagonalizable .....as there are two distinct eigen values

in 3rd case it is nilportent

but it is not possible both diagonalizable and nilpotent at the same time