Advertisements
Advertisements
प्रश्न
Matrix multiplication is commutative.
विकल्प
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
If AB is defined, it is not necessary that BA is defined.
Also if AB and BA are defined, it not”necessary that they have same order.
Further if AB and BA are defined and have same order, it is not necessary their corresponding elements are equal.
So, in general AB^BA
APPEARS IN
संबंधित प्रश्न
If \[\begin{pmatrix}a + 4 & 3b \\ 8 & - 6\end{pmatrix} = \begin{pmatrix}2a + 2 & b + 2 \\ 8 & a - 8b\end{pmatrix},\] ,write the value of a − 2b.
If A is square matrix such that A2 = A, show that (I + A)3 = 7A + I..
If A is a square matrix such that A2 = I, then (A – I)3 + (A + I)3 –7A is equal to ______.
Matrix addition is associative as well as commutative.
If A and B are two square matrices of the same order, then A + B = B + A.
(AB)–1 = A–1. B–1, where A and B are invertible matrices satisfying commutative property with respect to multiplication.
If `"A" = [("a","b"),("b","a")]` and `"A"^2 = [(alpha,beta),(beta, alpha)]` then ____________.
If matrix A `= [("a","b","c"),("b","c","a"),("c","a","b")]` where a, b, c are real positive numbers, abc = 1 and ATA = I, then the value of a3 + b3 + c3 is ____________.
If matrices A and B are inverse of each other then ____________.
Matrices A and B will be inverse of each other only if
Let \[A=[a_{ij}]\] and \[B=[b_{ij}]\] be two matrices of the same order \[m\times n\]. If \[C=A+B=[c_{ij}]\], which entry rule defines \[C\]?
For matrices \[A=[a_{ij}]\] and \[B=[b_{ij}]\] of the same order \[m\times n\], what is the order of \[C=A+B\]?
Let \[A=[a_{ij}]\] and \[B=[b_{ij}]\] be matrices of the same order \[m\times n\]. If \[D=A-B=[d_{ij}]\], which rule defines \[D\]?
Which expression is equivalent to \[A-B\]?
When can matrices be added or subtracted?
Which equation states the commutative property of matrix addition?
Which equation expresses the additive identity property for a matrix \[A\]?
Which equation expresses the additive inverse property for a matrix \[A\]?
Given \[A=\begin{bmatrix}\sqrt{3}&1&-1\\2&3&0\end{bmatrix}\] and \[B=\begin{bmatrix}2&\sqrt{5}&1\\-2&3&\frac{1}{2}\end{bmatrix}\], find \[A+B\].
For \[A=\begin{bmatrix}1&2&3\\2&3&1\end{bmatrix}\] and \[B=\begin{bmatrix}3&-1&3\\-1&0&2\end{bmatrix}\], which matrix is \[-B\]?
If \[A=\begin{bmatrix}1&2&3\\2&3&1\end{bmatrix}\] and \[B=\begin{bmatrix}3&-1&3\\-1&0&2\end{bmatrix}\], find \[2A-B\].
Which statement correctly uses the zero matrix \[O\] as the additive identity?
