CSIR NET Mathematics 2022| Linear Algebra (4 NOVEMBER)

Let A & B be two n × n matrices over a field F then

The rank and signature of the quadratic form -xy + z² in three variables over the reals is

Let x and y in  non-zero column vectors. From the matrix A = xy^’ where y’ is transpose of y than the rank of A is

The matrix  is

Let P be a  matrix over the real field. Then, which of the statements is/are true?