CBSE Class 12-science Answered

n linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e.,

where a_ij represents the entry on the ith row and ith column of A. Equivalently, the trace of a matrix is the sum of its eigenvalues, making it an invariant with respect to chosen basis.

The use of the term trace arises from the German term Spur (cognate with the English spoor), which, as a function in mathematics, is often abbreviated to "Sp".

to solve problems u can go through following web page also :

http://planetmath.org/encyclopedia/TraceOfAMatrix.html