If A = begin{bmatrix} 1 & 0 0 & -1 end{bmatr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The statement that $AB 
eq BA$ does not hold for every pair of matrices $A$ and $B$ for which $AB$ and $BA$ are defined. For instance,if $A = \be

Vedclass · Accepted Answer

No,matrix multiplication can be commutative for some pairs of matrices.

Vedclass · Answer

(B) The statement that $AB 
eq BA$ does not hold for every pair of matrices $A$ and $B$ for which $AB$ and $BA$ are defined. For instance,if $A = \begin{bmatrix} 1 & 0 \ 0 & 2 \end{bmatrix}$ and $B = \begin{bmatrix} 3 & 0 \ 0 & 4 \end{bmatrix}$,then: $AB = \begin{bmatrix} 1 	imes 3 + 0 	imes 0 & 1 	imes 0 + 0 	imes 4 \ 0 	imes 3 + 2 	imes 0 & 0 	imes 0 + 2 	imes 4 \end{bmatrix} = \begin{bmatrix} 3 & 0 \ 0 & 8 \end{bmatrix}$ $BA = \begin{bmatrix} 3 	imes 1 + 0 	imes 0 & 3 	imes 0 + 0 	imes 2 \ 0 	imes 1 + 4 	imes 0 & 0 	imes 0 + 4 	imes 2 \end{bmatrix} = \begin{bmatrix} 3 & 0 \ 0 & 8 \end{bmatrix}$ Since $AB = BA$,matrix multiplication is commutative in this case. Thus,the multiplication of diagonal matrices of the same order is commutative.

Similar Questions

If $A = \begin{bmatrix} \cos \frac{2 \pi}{33} & \sin \frac{2 \pi}{33} \\ -\sin \frac{2 \pi}{33} & \cos \frac{2 \pi}{33} \end{bmatrix}$,then $A^{2017} = $

Which of the given values of $x$ and $y$ make the following pair of matrices equal?
$\left[\begin{array}{cc}3x+7 & 5 \\ y+1 & 2-3x\end{array}\right]=\left[\begin{array}{cc}0 & y-2 \\ 8 & 4\end{array}\right]$

If $A = \begin{bmatrix} 1 & 2 & 3 \\ -2 & 3 & -1 \\ 3 & 1 & 2 \end{bmatrix}$ and $I$ is a unit matrix of $3^{rd}$ order,then $(A^2 + 9I)$ equals

If $A = [1, 2, 3]$,$B = \begin{bmatrix} 2 \\ 3 \\ 4 \end{bmatrix}$ and $C = \begin{bmatrix} 1 & 5 \\ 0 & 2 \end{bmatrix}$,then which of the following is defined?

If $A = \begin{bmatrix} 1 & 1 \\ 1 & 1 \end{bmatrix}$,then $A^{10}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module