Matrices

Let A be a square matrix such that AAT=I. Then 12A [ (A+AT )2+ (A-AT )2 ] is equal to

1. A2+AT
2. A3+I
3. A3+AT
4. A2+I

Consider the matrix f(x)= bmatrix x & - x & 0\ x & x & 0\ 0 & 0 & 1 bmatrix. Given below are two statements : In the light of the above statements, choose the correct answer from the options given below :

1. Statement I is false but Statement II is true
2. Both Statement I and Statement II are false
3. Both Statement I and Statement II are true
4. Statement I is true but Statement II is false

Let A be a 2 2 real matrix and I be the identity matrix of order 2. If the roots of the equation |A-xI|=0 be -1 and 3, then the sum of the diagonal elements of the matrix A2 is .