Question

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 1

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.