Let `A=[a_(ij)]` be a square matrix of order n such that `{:a_(ij)={(0," if i ne j),(i,if i=j):}` Statement -2 : The inverse of A is the matrix `B=[b_(ij)]` such that `{:b_(ij)={(0," if i ne j),(1/i,if i=j):}` Statement -2 : The inverse of a diagonal matrix is a scalar matrix.A. Statement -1 is True, Statement -2 is true, Statement -2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement -2 is True, Statement -2 is not a correct explanation for Statement -1.C. Statement -1 is True, Statement -2 is False.D. Statement -1 is False, Statement -2 is True.

Let `A=[a_(ij)]` be a square matrix of order n such that `{:a_(ij)={(0

1.	Let `A=[a_(ij)]` be a square matrix of order n such that `{:a_(ij)={(0," if i ne j),(i,if i=j):}` Statement -2 : The inverse of A is the matrix `B=[b_(ij)]` such that `{:b_(ij)={(0," if i ne j),(1/i,if i=j):}` Statement -2 : The inverse of a diagonal matrix is a scalar matrix.A. Statement -1 is True, Statement -2 is true, Statement -2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement -2 is True, Statement -2 is not a correct explanation for Statement -1.C. Statement -1 is True, Statement -2 is False.D. Statement -1 is False, Statement -2 is True.
Answer» Correct Answer - C We know that the inverse of a diagonal matrix `D=diag (d_1,d_2,d_3,…,d_n)` is a diagonal matrix given by `D^(-1)=diag (d_1^(-1),d_2^(-1),d_3^(-1),…,d_n^(-1))` `:. B=[b_(ij)]` is given by `{:b_(ij)={(0," if i ne j),(1/i,if i=j):}` Hence, statement -1 is true and statement -2 is false.

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