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Two matrices are said to be equal if they have the same order and each element of one is equal to the corresponding element of the other.
An m x n matrix A is said to be a square matrix if m = n i.e. number of rows = number of columns.
In a square matrix the diagonal from left hand side upper corner to right hand side lower corner is known as leading diagonal or principal diagonal.
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 = [aij]n×n, then tr(A) = ∑ni=1 aii = a11 + a22 +......+ ann.
For a square matrix A = [aij]n×n, if all the elements other than in the leading diagonal are zero i.e. aij = 0, whenever i ≠ j then A is said to be a diagonal matrix.
A matrix A = [aij]n×n is said to be a scalar matrix if aij = 0, i ≠ j
= m, i = j, where m ≠ 0
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