Transpose of a Matrix
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Matrices A and B will be inverse of each other only if
A. AB = BA
C. AB = 0, BA = I
B. AB = BA = 0
D. AB = BA = I
Let A and B be square matrices of order 3x3. Is (AB)2=A2B2? Give reasons.
If A is a square matrix of order 3 and determinant of A=3 find (AA^T)
What is a rank matrix?
If is a matrix satisfying then the values of and are
-1, -2
- Minimum number of zeros in A are 15.
- Minimum number of zeros in A are 10.
- Maximum number of zeros in A are 25.
- Maximum number of zeros in A are 24.
- 5A+10B=2I3
- 3A+2B=2I3
- 10A+5B=3I3
- 3A+6B=2I3
- cos(2aπ)
- sin(4aπ)
- cos(4aπ)
- sin(2aπ)
Let , , , , , and where denotes the transpose of the matrix . Then which of the following options is/are correct?
is an invertible matrix
The sum of diagonal entries of is
If then
is a symmetric matrix
If A is a matrix of order m x n then the order of AT where, AT is the transpose of A is
m x m
m x n
n x n
n x m
- m×m
- n×n
- n×m
- m×n
A square matrix A is called an orthogonal matrix if
AI =A
AAT=ATA=I
A2 = I
A(AT)T = I
- maximum number of non-zero elements in A are 6.
- maximum number of non-zero elements in A are 7.
- maximum number of distinct elements in A are 7.
- maximum number of distinct elements in A are 6.
(a) A2 − B2
(b) A2 − BA − AB − B2
(c) A2 − B2 + BA − AB
(d) A2 − BA + B2 + AB
- p3−5p
- p3−p2
- 2p2
- p3−3p
- M N
- −N2
- M2
- −M2
If matrix, and , then
but not
or
If A is a matrix of order m x n and B is a matrix of order l x p. The product AB of two matrices is defined if,
n = p
m = p
m = l
n = l
If then
Let and be two non-singular skew-symmetric matrices such that . If denotes the transpose of , then is equal to?
- A satisfies A2=A and A is of even order
- A satisfies A2=I and A is of odd order
- A2=2A
- A satisfies AA′=I and A is of even order
- 12
- 13
- 16
- 1
- A is a skew-symmetric matrix and |A|=0
- A is a symmetric matrix and |A|=0
- A is a symmetric matrix and |A|≠0
- None of these
If then the value
None of these
By using properties of determinants, show that: