Mathematics

Problem

The product

PQ

is defined but the product

QP

is not defined. Which statement about the possible orders of

P

and

Q

is necessarily true? a)

P

and

Q

are both square matrices of the same order b)

P

m \times n

and

Q

p \times m

with

n = p

P

m \times n

and

Q

n \times p

with

m \neq p

d) The number of columns of

P

equals the number of columns of

Q