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 : 
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 : 
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 