A matrix denotes a number.
False
Matrices of any order can be added.
False
Two matrices are equal if they have same number of rows and same number of columns.
False
Matrices of different order can not be subtracted.
True
Matrix addition is associative as well as commutative.
True
Matrix multiplication is commutative.
False
A square matrix where every element is unity is called an identity matrix.
False
If A and B are two square matrices of the same order, then A + B = B + A.
True
If A and B are two matrices of the same order, then A − B = B − A.
False
If matrix AB = O, then A = O or B = O or both A and B are null matrices.
False
Transpose of a column matrix is a column matrix.
False
If A and B are two square matrices of the same order, then AB = BA.
False
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
True
If A and B are any two matrices of the same order, then (AB)' = A'B'.
False
If (AB)' = B'A', where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.
True
If A, B and C are square matrices of same order, then AB = AC always implies that B = C.
False
AA' is always a symmetric matrix for any matrix A.
True
If A = \( \begin{bmatrix} 2 & 3 & -1 \\ 1 & 4 & 2 \end{bmatrix} \) and B = \( \begin{bmatrix} 2 & 3 \\ 4 & 5 \\ 2 & 1 \end{bmatrix} \), then AB and BA are defined and equal.
False
If A is skew symmetric matrix, then A\(^2\) is a symmetric matrix.
True
(AB)-1 = A-1 B-1, where A and B are invertible matrices satisfying commutative property with respect to multiplication.
True