_____ matrix is both symmetric and skew symmetric matrix.
Null matrix
Sum of two skew symmetric matrices is always _____ matrix.
Skew symmetric matrix
The negative of a matrix is obtained by multiplying it by _____.
-1
The product of any matrix by the scalar _____ is the null matrix.
0
A matrix which is not a square matrix is called a _____ matrix.
Rectangular matrix
Matrix multiplication is _____ over addition.
Distributive
If A is a symmetric matrix, then A\(^3\) is a _____ matrix.
Symmetric matrix
If A is a skew symmetric matrix, then A\(^2\) is a ____.
Symmetric matrix
If A is skew symmetric, then kA is a _____ (k is any scalar).
Skew symmetric matrix
If A is symmetric matrix, then B'AB is ____.
Symmetric matrix
If A and B are symmetric matrices of same order, then AB is symmetric if and only if ____.
AB = BA
In applying one or more row operations while finding A\(^{-1}\) by elementary row operations, we obtain all zeros in one or more, then A\(^{-1}\) ____.
does not exist
If A and B are square matrices of the same order, then (i) (AB)' = ____.
B' A'
(ii) (kA)' = ____ (k is any scalar)
kA
(iii) [k(A − B)]' = ____.
k(A − B)
If A and B are symmetric matrices, then (i) AB − BA is a ____.
Skew symmetric matrix
(ii) BA − 2AB is a ____.
neither symmetric nor skew symmetric matrix