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WorksheetsXII - Matrices - NCERT Exemplar Book
Total questions: 64
Worksheet time: 32mins
only AB is defined
only BA is defined
AB and BA both are defined
AB and BA both are not defined
scalar matrix
diagonal matrix
unit matrix
square matrix
If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a
Skew symmetric matrix
Null matrix
symmetric matrix
None of these
If A and B are two skew-symmetric matrices of the same order, then AB is a symmetric matrix if AB=BA.
True
False
If A and B are matrices of the same order, then (3A –2B)′ is equal to ________.
State True or False: The addition of matrices is defined if the order of the matrices is different.
True
False
State True or False: If two matrices A and B are of the same order, then 2A + B = B + 2A.
True
False
State True or False: Matrix subtraction is associative
True
False
True
False
State True or False:
For any three matrices of same order, AB = AC ⇒ B = C
True
False
square matrix
diagonal matrix
unit matrix
none
Total number of possible matrices of order 3×3 with each entry 2 and 0 is…..
9
27
81
512
3,1
2,3
2,4
3,3
I
O
2I
21I
If A and B are two matrices of the order 3×m and 3×n
respectively, and m = n, then the order of matrix (5A-2B) is….
m×3
3×3
m×n
3×n
I
A
O
NONE OF THESE
identity matrix
symmetric matrix
skew symmetric matrix
zero matrix
diagonal matrix
symmetric matrix
skew-symmetric matrix
scalar matrix
If A is matrix of order m × n and B is a matrix such that AB′ and B′A are both defined, then order of matrix B is
m × m
n × n
n × m
m × n
If A and B are matrices of same order, then (AB′–BA′) is a
skew-symmetric matrix
Null matrix
symmetric matrix
Unit matrix
A
I+A
I-A
3A
For any two matrices A and B:
AB=BA
AB ≠ BA
AB=O
None of these
State True or False:
UNIT matrix is a both symmetric and skew-symmetric matrix.
True
False
State True or False:
The Sum of two skew-symmetric matrices is always a symmetric matrix.
True
False
State True or False:
The negative of a matrix is obtained by multiplying it by -1.
True
False
State True or False:
The product of any matrix by the scalar 1 is the null matrix.
True
False
State True or False:
A matrix that is not a square matrix is called a null matrix.
True
False
State True or False:
Matrix multiplication is distributive over addition.
True
False
Fill in the blank:
If A is a symmetric matrix, then A^3 is a _________ matrix.
Null Matrix
Symmetric Matrix
Skew-symmetric matrix
Unit Matrix
State True or False:
If A is a skew-symmetric matrix, then A^2 is also a skew-symmetric matrix.
True
False
If A and B are square matrices of the same order, then
(AB)′ = _________.
B’A’
A’ B’
If A and B are square matrices of the same order, then
(kA)′ = _________. (k is any scalar)
kA’
k1A′
If A and B are square matrices of the same order and k is any scalar, then [k (A – B)]′ = _________.
k1(A′−B′)
k(A'-B')
If A is skew-symmetric, then kA is a _________. (k is any scalar)
Symmetric Matrix
Skew-symmetric Matrix
If A and B are symmetric matrices, then
AB – BA is a _________.
Symmetric Matrix
Skew-symmetric Matrix.
State True or False:
If A and B are symmetric matrices, then BA – 2AB is a skew-symmetric matrix.
True
False
State True or False:
If A is a symmetric matrix, then B′AB is also a symmetric matrix.
True
False
If A and B are symmetric matrices of same order, then AB is symmetric if and only if _________.
AB=BA
AB ≠ BA
AB=I
AB=O
is a null matrix.
is a unit matrix
doesn't exist
can't say anything.
State True or False:
A matrix denotes a number.
True
False
State True or False:
Matrices of any order can be added.
True
False
State True or False:
Two matrices are equal if they have the same number of rows and the same number of columns.
True
False
State True or False:
Matrices of different orders can not be subtracted.
True
False
State True or False:
Matrix addition is associative as well as commutative.
True
False
State True or False:
Matrix multiplication is commutative.
True
False
State True or False:
A square matrix where every element is unity is called an identity matrix.
True
False
State True or False:
If A and B are two square matrices of the same order, then A + B = B + A.
True
False
State True or False:
If A and B are two matrices of the same order, then A – B = B – A.
True
False
State True or False:
If matrix AB = O, then A = O or B = O or both A and B are null matrices.
True
False
State True or False:
The transpose of a column matrix is a column matrix.
True
False
State True or False:
If A and B are two square matrices of the same order, then AB = BA.
True
False
State True or False:
If each of the three matrices of the same order is symmetric, then their sum is a symmetric matrix.
True
False
State True or False:
If A and B are any two matrices of the same order, then (AB)′ = A′B′.
True
False
State True or False:
If (AB)′ = B′ A′, where A and B are not square matrices, then the number of rows in A is equal to the number of columns in B and the number of columns in A is equal to number of rows in B
True
False
State True or False:
If A, B, and C are square matrices of the same order, then AB = AC always implies that B = C.
True
False
State True or False:
AA′ is always a symmetric matrix for any matrix A.
True
False
True
False
True
False
True
False
State True or False: If A is a symmetric matrix, then B′AB is also a symmetric matrix.
True
False
