How would one solve a question of this nature?
We know that given an arbitrary square matrix, A, that a matrix B is said to be congruent to A if there exists a nonsingular (invertible) matrix P such that B = (P^T)AP.
Also, a matrix B is equivalent to a matrix A if B can be obtained from A by a sequence of elementary row and column operations. Alternatively, B is equivalent to A if there exist nonsingular matrices P and Q such that B = PAQ. Just like row and column equivalence, equivalence of matrices is an equivalence relation.