Advertisements
Advertisements
Question
If A and B are any two matrices of the same order, then (AB)′ = A′B′.
Options
True
False
Advertisements
Solution
This statement is False.
Explanation:
Since (AB)' = B'A'.
APPEARS IN
RELATED QUESTIONS
If A' = `[(3, 4),(-1, 2),(0, 1)]` and B = `[(-1, 2, 1),(1, 2, 3)]`, then verify that (A + B)' = A' + B'
If A' = `[(-2, 3),(1, 2)]` and B = `[(-1, 0),(1, 2)]`, then find (A + 2B)'
For the matrices A and B, verify that (AB)′ = B'A', where A = `[(1),(-4),(3)]`, B = `[(-1, 2, 1)]`
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.
For the matrix A = `[(1, 5),(6, 7)]` verify that (A + A') is a symmetric matrix.
For the matrix A = `[(1, 5),(6, 7)]`, verify that (A – A') is a skew symmetric matrix.
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(6, -2, 2),(-2, 3, -1),(2, -1, 3)]`
Express the following matrices as the sum of a symmetric and a skew symmetric matrix:
`[(1, 5),(-1, 2)]`
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.
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.
If A is a square matrix, then AA is a
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
If A and B are matrices of the same order, then ABT − BAT is a
The matrix \[A = \begin{bmatrix}0 & - 5 & 8 \\ 5 & 0 & 12 \\ - 8 & - 12 & 0\end{bmatrix}\] is a
The matrix \[A = \begin{bmatrix}1 & 0 & 0 \\ 0 & 2 & 0 \\ 0 & 0 & 4\end{bmatrix}\] is
If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.
If A and B are symmetric matrices of the same order, then (AB′ –BA′) is a ______.
The matrix `[(0, -5, 8),(5, 0, 12),(-8, -12, 0)]` is a ______.
Sum of two skew-symmetric matrices is always ______ matrix.
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 A, B are Symmetric matrices of same order, then AB – BA is a
If A = [aij] is a skew-symmetric matrix of order n, then ______.
If ax4 + bx3 + cx2 + dx + e = `|(2x, x - 1, x + 1),(x + 1, x^2 - x, x - 1),(x - 1, x + 1, 3x)|`, then the value of e 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 ______.
Which of the following is correct?
A square matrix \[A=[a_{ij}]_{n\times n}\] is symmetric when which condition holds?
A square matrix \[A=[a_{ij}]_{n\times n}\] is skew-symmetric when which condition holds?
What must be true of every diagonal element of a skew-symmetric matrix?
If \[C=A-A^T\] for a square matrix \[A\], what is \[C^T\]?
Which expression writes any square matrix \[A\] as the sum of a symmetric and a skew-symmetric matrix?
Why does multiplying \[A+A^T\] by \[\frac{1}{2}\] not change its symmetric property?
For \[B=\begin{bmatrix}2&-2&-4\\-1&3&4\\1&-2&-3\end{bmatrix}\], what is its skew-symmetric part \[Q=\frac{1}{2}(B-B^T)\]?
