If A = [ aij ] is a square matrix of order n, then elements( entries) a11, a22,..., ann are said to constitute the diagonal, of the matrix A. Note: diagonal elements come only in case of Square matrix
Diagonal Matrices: A square matrix B = [ bij ] m × m is said to be a diagonal matrix if all its non diagonal elements are zero. That is a matrix B = [ bij ] m × m is said to be a diagonal matrix if bij = 0, when i ≠ j.
Scalar Matrices: A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal. That is, a square matrix B = [ bij ] n × n is said to be a scalar matrix if
o bij = 0, when i ≠ j o bij = k, when i = j, for some constant k.
Identity Matrices: A square matrix in which elements in the diagonal are all 1 and rest is all zero is called an identity matrix. We denote the identity matrix of order n by In. Observe that a scalar matrix is an identity matrix when k = 1. But every identity matrix is clearly a scalar matrix.
Zero Matrices: A matrix is said to be zero matrix or null matrix if all its elements are zero. We denote zero matrix by O.