Mathematics

Problem

Four matrices

P

Q

R

and

S

have respective orders

x \times y

y \times z

z \times t

and

t \times x

, where

x, y, z, t

are positive integers. a. (i) Show that the product

PQRS

is defined and determine its order. b. (ii) Prove that

PQRS

is always a square matrix, whatever positive integer values

x, y, z, t

may take. c. (iii) Derive an expression, in terms of

x

, for the total number of elements contained in

PQRS

. d. (iv) Verify your result in part (iii) for the specific choice

x=4,\; y=2,\; z=5,\; t=4