where x and y are real numbers and addition
and multiplication are defined according to the usual rules for
adding and multiplying matrices.
(a) Add and multiply the matrices
æ ç
è
x
-y
y
x
ö ÷
ø
and
æ ç
è
u
-v
v
u
ö ÷
ø
.
(b) What are the identities and inverses for addition and multiplication?
(c) Consider also the subset R* for which y=0. Investigate the
arithmetic of R* (addition, subtraction, multiplication, division,
identities, inverses, distributive law) and compare it with the arithmetic
of real numbers.
(d) Compare the arithemetic of
C* with that of complex numbers.
(e) The matrix
æ ç
è
-1
0
0
-1
ö ÷
ø
is equivalent to the real number -1. What is the matrix equivalent to