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 .