example of trace of a matrix

Let $A=\\left[\\begin{array}[]{ccc}2&4&6\\\\8&10&12\\\\14&16&18\\end{array}\\right]$ , $A^{\\prime}=\\frac{1}{2}A=\\left[\\begin{array}[]{ccc}1&2&3\\\\4&5&6\\\\7&8&9\\end{array}\\right]$ and $B=\\left[\\begin{array}[]{ccc}9&8&7\\\\6&5&4\\\\3&2&1\\end{array}\\right]$ then

	$\\displaystyle\\operatorname{trace}(A+B)$	$\\displaystyle=\\operatorname{trace}(A)+\\operatorname{trace}(B)$
		$\\displaystyle=(2+10+18)+(9+5+1)$
		$\\displaystyle=45$

	$\\displaystyle\\operatorname{trace}(A)$	$\\displaystyle=\\operatorname{trace}(2A^{\\prime})$
		$\\displaystyle=2\\cdot\\operatorname{trace}(A^{\\prime})$
		$\\displaystyle=2\\cdot\\operatorname{trace}\\left[\\begin{array}[]{ccc}1&2&3\\\\4&5&6\\\\7&8&9\\end{array}\\right]$
		$\\displaystyle=2\\cdot(1+5+9)$
		$\\displaystyle=30$