Chapter 4.3, Problem 36E

Determining Subspace of $M_{n,n}$ In Exercises $29-36$, determine whether the subset of $M_{n,n}$is a subspace of $M_{n,n}$with the standard operations. Justify your answer.

The set of all $n\times n$ matrices whose trace is nonzero

(Recall that the trace of a matrix is the sum of the main diagonal entries of the matrix.)