1) To verify that the matrix is equivalent to matrix I3
Just check whether the matrix has reversed?
2) Determine the nullity of the matrix?
I guess you are talking about the identity matrix $\displaystyle 3\times 3$, right? If so, just check out if your matrix is inversible. If it has an inverse then it is equivalent to the $\displaystyle 3\times 3$ matrix, otherwise no.1) To verify that the matrix is equivalent to matrix I3
And if you find that your matrix is equivalent to the null matrix then it's obvious that it's not equivalent to the identity matrix.