Mathematics

Problem

Matrices

X

Y

and

Z

have orders

4 \times 3

3 \times 2

and

2 \times 6

respectively. a. (i) Determine the order of the product

XYZ

. b. (ii) Calculate the total number of elements in each of the matrices

XY

YZ

and

XYZ

. c. (iii) Find the ratio of the number of elements in

XY

to that in

XYZ

. d. (iv) If all the entries of

XY

are replaced by their negatives, does the order of the matrix change? State the reason briefly.