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(iv), , Ww), , wi), , Diagonal matrix, A square matrix B = [b,)_, , diagonal elements are zero, that isa matrix B = (6,) ., matrix if b, = 0, when i # j, , is said to be a diagonal matrix if all its non, is said to be a diagonal, , , , “1100, , For example, A= [4], p-l! lcelo 20 . are diagonal matrices, lo 2, 0 03, of order 1, 2, 3, respectively., Scalar matrix, , A diagonal matrix is said to be a scalar matrix if its diagonal elements are equal,, that is, a square matrix B = (6,], ,, is said to be a scalar matrix if, , , , when i #j, when i = j, for some constant k., For example, [Bo 0, A=). {3 ‘I c= 0 Vi oO, 0-1, Lo o Vi., are scalar matrices of order 1, 2 and 3, respectively., Identity matrix, , A square matrix in which elements in the diagonal are all 1 and rest are all zero, is called an identity matrix. In other words, the square matrix A =[a,) is an, , oe 1 if i=, identity matissif y= Vy ig gy:, , ‘We denote the identity matrix of order n by I, When order is clear from the, context, we simply write it as 1., , , , 00, 10, Forexamle i |p i}. 7 ; : are identity matrices of order 1, 2 and 3,, , respectively., Observe that a scalar matrix is an identity matrix when k = 1. But every identity, matrix is clearly a scalar matrix.