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 is a skew symmetric matric of order 3, then prove that det A = 0
If A' = `[(-2, 3),(1, 2)]` and B = `[(-1, 0),(1, 2)]`, then find (A + 2B)'
Show that the matrix A = `[(1, -1, 5),(-1, 2, 1),(5, 1, 3)]` is a symmetric matrix.
Show that the matrix A = `[(0, 1, -1),(-1, 0, 1),(1, -1, 0)]` is a skew symmetric matrix.
Find `1/2` (A + A') and `1/2` (A – A'), when A = `[(0, a, b),(-a, 0, c),(-b, -c, 0)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(3, 5),(1, -1)]`
If A and B are symmetric matrices, prove that AB – BA is a skew symmetric matrix.
Find the values of x, y, z if the matrix A = `[(0, 2y, z),(x, y, -z),(x, -y, z)]` satisfy the equation A'A = I.
Show that all the diagonal elements of a skew symmetric matrix are zero.
If A and B are symmetric matrices of the same order, write whether AB − BA is symmetric or skew-symmetric or neither of the two.
Write a square matrix which is both symmetric as well as skew-symmetric.
If a matrix A is both symmetric and skew-symmetric, then
If A = [aij] is a square matrix of even order such that aij = i2 − j2, then
If A and B are two matrices of order 3 × m and 3 × n respectively and m = n, then the order of 5A − 2B is
The matrix \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is
If A = `[(cosalpha, sinalpha),(-sinalpha, cosalpha)]`, and A–1 = A′, find value of α
The matrix `[(1, 0, 0),(0, 2, 0),(0, 0, 4)]` is a ______.
The matrix `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.
______ matrix is both symmetric and skew-symmetric matrix.
If A and B are symmetric matrices, then AB – BA is a ______.
If A is symmetric matrix, then B′AB is ______.
If A and B are symmetric matrices of same order, then AB is symmetric if and only if ______.
If each of the three matrices of the same order are symmetric, then their sum is a symmetric matrix.
AA′ is always a symmetric matrix for any matrix A.
If P is of order 2 x 3 and Q is of order 3 x 2, then PQ is of order ____________.
If A and B are symmetric matrices of the same order, then ____________.
If A and B are symmetric matrices of the same order, then ____________.
If A = `[(3, "x" - 1),(2"x" + 3, "x" + 2)]` is a symmetric matrix, then x = ____________.
If A `= [(6,8,5),(4,2,3),(9,7,1)]` is the sum of a symmetric matrix B and skew-symmetric matrix C, then B is ____________.
Number of symmetric matrices of order 3 × 3 with each entry 1 or – 1 is ______.
If A and B are symmetric matrices of the same order, then AB – BA is ______.
