Consider the following two statements with respect to the matrices A_{m $$\times$$ n ,} B_{n $$\times$$ m} , C_{n$$\times$$ n} and Dn _{$$\times$$ n} .

Statement 1 : tr(AB) = tr(BA)

Statement 2 : tr(CD) = tr(DC)

where tr( ) represents the trace of a matrix. Which one of the following holds?

Which of the following statements is/are TRUE for a group G?

Consider a simple undirected graph of 10 vertices. If the graph is disconnected, then the maximum number of edges it can have is __________.

The number of arrangements of six identical balls in three identical bins is ___________.