If A and B are square matrices of size n x n, then which of the following statement is not true?
A.  det. (AB) = det (A) det (B) 
B.  det (kA) = k^{n} det (A) 
C.  det (A + B) = det (A) + det (B) 
D.  det (A^{T}) =1/det (A^{1}) 
Option: C Explanation : Click on Discuss to view users comments. JAGADEESH said: (3:04am on Saturday 23rd December 2017)
}if A={1,2:3,4}= Bdet A=2det B=2det (A B)=8hence proved

In the matrix equation Px = q. which of the following is a necessary condition for the existence of at least one solution for the unknown vector x?
A.  Augmented matrix [Pq] must have the same rank as matrix P 
B.  Vector q must have only nonzero elements 
C.  Matrix P must be singular 
D.  None of these 
Option: A Explanation : Click on Discuss to view users comments. 
Rank of the diagonal matrix
A.  1 
B.  2 
C.  3 
D.  4 
Option: D Explanation : Since the number of nonzero elements on this diagonal matrix is four, hence the rank is four. Click on Discuss to view users comments. 
Matrix, A =

A.  orthogonal 
B.  nonsingular 
C.  have A^{1} exists 
D.  both (b) & (c) 
Option: D Explanation : Determinant A = 1 (cos2Θ + sin2Θ) Hence A is nonsingular and A^{1 }exists Click on Discuss to view users comments. hmaza said: (10:19pm on Monday 29th April 2013)
singular means det is zero but answer b and c is true
