
A-6 Mathematical Methods
31. If A is a nonsingular matrix with l
i
as its eigen-
values then the eigenvalues of Adj A are
(a)
1
i
λ
(b)
i
A
λ
(c) l
2
i
(d) l
−2
i
Ans: (b)
32. If
12
21
A
⎡⎤
=
⎢⎥
−
⎣⎦
then A
4
= xI where x =
(a) 1 (b) 5 (c) 25 (d) 625 Ans: (c)
CHAPTER 3 REAL AND COMPLEX MATRICES
Symmetric/Skew-Symmetric
1. If A and B are nth order symmetric matrices
then B
T
AB is a/an _______ matrix.
(a) Singular (b) Skew-symmetric
(c) Symmetric (d) Orthogonal Ans: (c)
2. If A is a nonsingular symmetric matrix then
A
−1
is a/an ______ matrix.
(a) Skew-symmetric (b) Symmetric
(c) Orthogonal (d) Unit Ans: (b)
3. If A and B are symmetric and are commuta- ...