1. For the square matrix

show that A (adj A) = |A|I

2. Find the inverse of

3.If

and

, find B.

4. If

show that A is an orthogonal, that is

.

5. Find the inverse of

6. Given two matrices where

and

,

verify

.

7. Using matrices, solve the equations

x+y+2z = 4
2x-y+3z = 9
3x-y-z=2.

8. If the matrix A is fiven by

,
prove that it satisfies the relation

where I stands for the unit matrix of order 2.

9. If

and

,

prove that

.

10.Express

as the sum of a symmetric and skew symmetric matrices.
A symmetric matrix is a square matrix if (i,j)th element of A is equal to (j,i)th element of A.
A skew symmetric matric is a square matrix if the (i,j)th element of A is equal to the negative of the (j,i)th element of A.