Chapter 1: Applications of Matrices and Determinants - Online Test
Q1. If AT A−1 is symmetric, then A2
=
Answer : Option B
Explaination / Solution:
Q2. If A is a
non-singular matrix such that A−1 = 
, then ( AT )−1 =
, then ( AT )−1 =
Answer : Option D
Explaination / Solution:
Q3. if A= 
, and AT = A−1 , then the value of x is
, and AT = A−1 , then the value of x is
Answer : Option A
Explaination / Solution:
Q4. if A= 
, and AB = I2 , then B=
, and AB = I2 , then B=
Answer : Option B
Explaination / Solution:
Q5. if A = 
, and A(adj A) = 
, then k=
, and A(adj A) = , then k=
Answer : Option D
Explaination / Solution:
Q6. If A= 
, be such that λ A−1 = A ,
then λ is
, be such that λ A−1 = A ,
then λ is
Answer : Option C
Explaination / Solution:
Q7. If adj A= 
, adj
B= 
, then adj ( AB) is
, adj
B= , then adj ( AB) is
Answer : Option B
Explaination / Solution:
Q8. The rank of the matrix 
is
is
Answer : Option A
Explaination / Solution:
Q9. If xa yb
= em , xc yd
= en , 
then the values of x and y are respectively,
then the values of x and y are respectively,
Answer : Option D
Explaination / Solution:
Q10.
Which of the following is/are correct?
(i) Adjoint of a
symmetric matrix is also a symmetric matrix.
(ii) Adjoint of a
diagonal matrix is also a diagonal matrix.
(iii) If A is a square
matrix of order n and λ is a scalar, then adj( λ A) = λn
adj( A) .
(iv) A(adjA) = (adjA)
A =| A | I
Answer : Option D
Explaination / Solution:
