Advertisements
Advertisements
Question
If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if ______.
Advertisements
Solution
If A and B are two skew-symmetric matrices of same order, then AB is symmetric matrix if AB = BA.
APPEARS IN
RELATED QUESTIONS
If A = `[(-1, 2, 3),(5, 7, 9),(-2, 1, 1)]` and B = `[(-4, 1, -5),(1, 2, 0),(1, 3, 1)]`, then verify that (A + B)' = A' + B'
If A = `[(-1, 2, 3),(5, 7, 9),(-2, 1, 1)]` and B = `[(-4, 1, -5),(1, 2, 0),(1, 3, 1)]`, then verify that (A – B)' = A' – B'
If A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A – B)' = A' – B'
For the matrices A and B, verify that (AB)′ = B'A' where A = `[(0),(1),(2)]`, B = `[(1, 5, 7)]`
Show that the matrix A = `[(1, -1, 5),(-1, 2, 1),(5, 1, 3)]` is a symmetric matrix.
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(3, 5),(1, -1)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(3, 3, -1),(-2, -2, 1),(-4, -5, 2)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(1, 5),(-1, 2)]`
If the matrix A is both symmetric and skew symmetric, then ______.
Show that all the diagonal elements of a skew symmetric matrix are zero.
If a matrix A is both symmetric and skew-symmetric, then
If A is a square matrix, then AA is a
If \[A = \begin{bmatrix}2 & 0 & - 3 \\ 4 & 3 & 1 \\ - 5 & 7 & 2\end{bmatrix}\] is expressed as the sum of a symmetric and skew-symmetric matrix, then the symmetric matrix is
Show that a matrix which is both symmetric and skew symmetric is a zero matrix.
If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.
If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α
Express the matrix `[(2, 3, 1),(1, -1, 2),(4, 1, 2)]` as the sum of a symmetric and a skew-symmetric matrix.
The matrix `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.
If A is a symmetric matrix, then A3 is a ______ matrix.
If A and B are symmetric matrices, then BA – 2AB is a ______.
AA′ is always a symmetric matrix for any matrix A.
If A is skew-symmetric matrix, then A2 is a symmetric matrix.
If A and B are symmetric matrices of the same order, then ____________.
If A is any square matrix, then which of the following is skew-symmetric?
Let A = `[(2, 3),(a, 0)]`, a ∈ R be written as P + Q where P is a symmetric matrix and Q is skew-symmetric matrix. If det(Q) = 9, then the modulus of the sum of all possible values of determinant of P is equal to ______.
If A and B are symmetric matrices of the same order, then AB – BA is ______.
A square matrix \[A=[a_{ij}]_{n\times n}\] is symmetric when which condition holds?
For a symmetric matrix \[A=[a_{ij}]_{n\times n}\], which entrywise relation is true for all \[i\] and \[j\]?
For a skew-symmetric matrix \[A=[a_{ij}]_{n\times n}\], which relation holds for all \[i\] and \[j\]?
If \[C=A-A^T\] for a square matrix \[A\], what is \[C^T\]?
Which identity is used to replace \[(A^T)^T\] by \[A\] when proving that \[A+A^T\] is symmetric?
Why does multiplying \[A+A^T\] by \[\frac{1}{2}\] not change its symmetric property?
For the matrices \[P=\frac{1}{2}(B+B^T)\] and \[Q=\frac{1}{2}(B-B^T)\], what is \[P+Q\]?
