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 matrix1) To verify that the matrix is equivalent to matrix I3, right? If so, just check out if your matrix is inversible. If it has an inverse then it is equivalent to the
matrix, otherwise no.
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.