3 Let A and B be 66 matrices where A a nd B b Find each of

3. Let A and B be 6*6 matrices where |A|= a nd |B| = b. Find each of the following a. |AB| b. |B^T| c. | (-2A)| d. |B^3|

Solution

a)

we |AB| = |A||B|

= a * b

= ab

b)

|B^T| = |B| = b

c)

|cA| = c^n |A| , where is the dimension of matrix

| (-2A) | = (-2)^6 * |A|

= 64 *a

= 64a

d)

| A^k| = |A|^k

=>

|B^3| = |B|^3

= b^3