Trace of a Square Matrix

1. The Trace of a Square Matrix is the Sum of All the Elements of it's Main Diagonal.
2. Given the Square Matrix \(A\) as follows
   
   \(A=\begin{bmatrix} a_{11} & a_{12} & ... & a_{1n}\\ a_{21} & a_{22} & ... & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\a_{m1} & a_{m2} & ... & a_{mn}\end{bmatrix}\)
   
   The Trace of Matrix \(A\) is calculated as
   
   \(Trace(A)=a_{11} + a_{22} + \cdots + a_{nn}\)
3. Following are some examples that show calculation of Trace of Square Matrices
   
   \(A= \begin{bmatrix} 3 & -2 & 1\\ 1 & -5 & 6\\ -4 & -7 & 2\end{bmatrix} \Rightarrow\) Trace(\(A\)) = \(3 - 5 + 2 = 0\)
   
   \(B= \begin{bmatrix} -4 & 5 \\ 1 & 9\end{bmatrix} \Rightarrow\) Trace(\(B\)) = \(-4 + 9 = 5\)