MATRICES

In a skew symmetric matrix, the diagonal elements are all
1. Different from each other
2. Zero
3. One
4. None
If I is a unit matrix, then 3I will be
1. A unit matrix
2. A triangular matrix
3. A scalar matrix
4. None
If A is a square matrix of order n and A=kB, where k is a scalar, then |A|=
1. |B|
2. k |B|
3. kⁿ |B|
4. n |B|
If A=dig(2,−1,3),B=dig(−1,3,2), then A²B=
1. dig (5, 4, 11)
2. dig (-4, 3, 18)
3. dig (3, 1, 8)
4. None
If A is a m×nmatrix and B is a matrix such that both AB and BA are defined, then the order of B is
1. m×n
2. n×m
3. m×m
4. n×n
If A and B are square matrices of order 2, then (A+B)²=
1. A²+2AB+B²
2. A²+2BA+B²
3. Both a & b
4. None
Which of the following relations is incorrect
1. (A+B+....+l)′=A′+B′+....+l′
2. (AB....l)′=A′B′....l′
3. (kA)′=kA′
4. (A)′=A
If AB=C, then matrices A,B,Care
1. A2×3,B3×2,C2×3
2. A3×2,B2×3,C3×2
3. A3×3,B2×3,C3×3
4. A3×2,B2×3,C3×3
If [m n][m]=[25] and m< n, then (m, n) =
n
1. (2, 3)
2. (3, 4)
3. (4, 3)
4. None
AB=0, if and only if
1. A≠O,B=O
2. A=O,B≠O
3. A=Oor B=O
4. None
If A and B are two matrices such that A+B and AB are both defined, then
1. Aand B are two matrices not necessarily of same order
2. A and B are square matrices of same order
3. Number of columns of A= Number of rows of B
4. None
If A and B are square matrices of same order, then
1. A+B=B+A
2. A+B=A−B
3. A−B=B−A
4. AB=BA
If A and B are two matrices and (A+B)(A−B)=A²−B², then
1. AB=BA
2. A²+B²=A²−B²
3. A′B′=AB
4. None
If A and B are two matrices such that AB=Band BA=A, then A²+B²=
1. 2AB
2. 2BA
3. A+B
4. AB
A,B are n-rowed square matrices such that AB=Oand B is non-singular. Then
1. A≠O
2. A=O
3. A=I
4. None
Which of the following is incorrect
1. A²−B²=(A+B)(A−B)
2. (Aⁿ)ⁿ=A
3. (AB)ⁿ=AⁿBⁿ,where A, B commute
4. ALL
Which one of the following is not true
1. Matrix addition is commutative
2. Matrix addition is associative
3. Matrix multiplication is commutative
4. Matrix multiplication is associative
The matrix product AB=O, then
1. A=Oand B=O
2. A=O or B=O
3. A is null matrix
4. None
If A and B are square matrices of order n × n, then (A−B)² is equal to
1. A²−B²
2. A²−2AB+B²
3. A²+2AB+B²
4. A²−AB-BA+B²
Choose the correct answer
1. Every identity matrix is a scalar matrix
2. Every scalar matrix is an identity matrix
3. Every diagonal matrix is an identity matrix
4. A square matrix whose each element is 1 is an identity matrix
If two matrices A and B are of order p × q and r × s respectively, can be subtracted only, if
1. p=q
2. p=q,r=s
3. p=r,q=s
4. None
A matrix in which the number of rows are equal to the number of columns, is said to be
1. Square matrix
2. Daigonal matrix
3. Scalar matrix
4. Identity matrix
A square matrix in which elements in the diagonal are all 1 and rest are all zero is called an
1. Square matrix
2. Daigonal matrix
3. Scalar matrix
4. Identity matrix
A square matrix B = [bij] m × m is said to be a ________ if all its non
diagonal elements are zero
1. Square matrix
2. Daigonal matrix
3. Scalar matrix
4. Identity matrix
A diagonal matrix is said to be a ____________ if its diagonal elements are equal
1. Square matrix
2. Daigonal matrix
3. Scalar matrix
4. Identity matrix
A matrix is said to be ____________ if all its elements are zero
1. Square matrix
2. Daigonal matrix
3. Scalar matrixv
4. Zero matrix
If A = [aij] be an m × n matrix, then the matrix obtained by interchanging the rows and columns of A is called the_____of A
1. Symmetric
2. Skew Symmetric
3. Transpose
4. None
A square matrix A = [aij] is said to be _________ if A′ = A.
1. Symmetric
2. Skew Symmetric
3. Transpose
4. None
A square matrix A = [aij] is said to be __________- matrix ifA′ = – A,
1. Symmetric
2. Skew Symmetric
3. Transpose
4. None
If A is a square matrix of order m, and if there exists another square matrix B of the same order m, such that AB = BA = I, then B is called the ________ matrix of A
1. Symmetric
2. Skew Symmetric
3. Transpose
4. Inverse

MATRICES

Quiz