The transpose of a matrix A, denoted by A^T, is obtained by
A
Multiplying all elements by -1
B
Interchanging rows and columns
C
Reversing all elements
D
Taking inverse of A
Analysis & Theory
Transpose is obtained by interchanging rows and columns.
If A is a 2×3 matrix, then A^T is of order
A
2×3
B
3×2
C
3×3
D
2×2
Analysis & Theory
If A is m×n, then A^T is n×m. So 2×3 becomes 3×2.
For any matrix A, (A^T)^T equals
A
A
B
A^T
C
I
D
A^2
Analysis & Theory
Taking transpose twice gives the original matrix: (A^T)^T = A.
If A = [ [1, 2], [3, 4] ], then A^T equals
A
[ [1, 2], [3, 4] ]
B
[ [1, 3], [2, 4] ]
C
[ [4, 3], [2, 1] ]
D
[ [2, 1], [4, 3] ]
Analysis & Theory
Transpose is found by interchanging rows and columns.
If A and B are of same order, then (A + B)^T equals
A
A^T + B^T
B
A^T - B^T
C
A^T B^T
D
None
Analysis & Theory
Transpose distributes over addition: (A + B)^T = A^T + B^T.
If k is a scalar and A is a matrix, then (kA)^T equals
A
k A^T
B
k^T A
C
k A
D
A^T
Analysis & Theory
Scalar multiplication commutes with transpose: (kA)^T = k(A^T).
For matrices A and B, (AB)^T equals
A
A^T B^T
B
B^T A^T
C
AB
D
None of these
Analysis & Theory
Transpose of product reverses order: (AB)^T = B^T A^T.
A matrix A is called symmetric if
A
A = A^T
B
A = -A^T
C
A^T = I
D
A^2 = A
Analysis & Theory
A symmetric matrix is equal to its transpose.
A matrix A is called skew-symmetric if
A
A = A^T
B
A = -A^T
C
Diagonal elements are zero
D
A^T = I
Analysis & Theory
A skew-symmetric matrix satisfies A^T = -A.
If A is an orthogonal matrix, then A^T equals
A
A
B
A^−1
C
I
D
−A
Analysis & Theory
For an orthogonal matrix, A^T = A^−1.