## 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?