# Trace of Matrix

The sum of the elements of a square matrix

*A*lying along the principal diagonal is called the trace of*A*, i.e., tr(*A*)Thus if

*A*= [*a*]_{ij}_{n}_{ Ã— n },_{ }thentr(

*A*) =# Properties of trace of a matrix

Let

*A*= [*a*]_{ij}_{n}_{ Ã— n}and*B*= [*b*]_{ij}_{n}_{ Ã— n}and*Î»*be a scalar, then- tr(
*Î»A*) =*Î»*tr(*A*) - tr(
*A*+*B*) = tr(*A*) + tr(*B*) - tr
*(AB*) = tr(*BA*)