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
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.
What name is given to the result?