Matrix Properties Exercise

1. Give an example of:

a. A 2 x 2 matrix and its additive inverse.
b. The identity element for addition for 2 X 2 matrices.
c. A 2 X 2 matrix and its multiplicative inverse.
d. The identity matrix for the multiplication of 2 X 2 matrices.

If A = , B = , C = , D = 

2.
 Calculate:
a.
 AB
b.
 BA
c.
 What property about 2 X 2 matrices do parts a and b show?
3.
 Calculate:
a.
 (AB)C
b.
 A(BC)
c,
 What property about 2 X 2 matrix multiplication do parts a and b show?
4.
 Find the determinant of:
a.
 A
b.
 B
c.
 AB
5.
 Find the multiplicative inverses of
a.
 A
b.
 B
c.
 BA

6. Find the multiplicative inverses of

a.
b.
c.

7. a. Calculate the matrix product: .

b. What is the special name for the matrix ?

c. Find the multiplicative inverse of the matrix .

8. R = 

(i) Find the determinant of R.
(ii) Find R-1, the multiplicative inverse of R
(iii) What should RR-1 be equal to?

9. A = 

(i) What is the determinant of A?
(ii) Write down A-1 , the multiplicative inverse of A.
(iii) B = . Calculate AB.

10. Calculate 

What name is given to the result?