Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Which of the following is true for AxB if <img alt="A=\left[\begin{array}{rr}{4} & {3} \\ {5} & {4}\end{array}\right]\;\;\text{and}\;\;B=\left[\begin{array}{cc}{-4} & {3} \\ {\;\;\

Which of the following is true for AxB if A=\left[\begin{array}{rr}{4} & {3} \\ {5} & {4}\end{array}\right]\;\;\text{and}\;\;B=\left[\begin{array}{cc}{-4} & {3} \\ {\;\;\;5} & {-4}\end{array}\right]

Option: 1

A\times B=B\times A


Option: 2

A \times B=-I


Option: 3

A=B^{-1}


Option: 4

All of the above


Answers (1)

best_answer

 

 

Properties of matrix multiplication -

Properties of matrix multiplication:

    i) Multiplication may or may not be commutative so AB may be equal to or may not be equal to BA.    

    ii) Matrix multiplication is associative, meaning A(BC) = (AB)C

    iii) Matrix multiplication is distributive over addition, mean  A(B+C) = AB + AC   

    iv) if matrix multiplication of two matrices gives null matrix then it doesn’t mean that any of those two matrices was a null matrix. So         AB = O ? A = O or B = O.

        

 

    v) Cancellation law in matrix multiplication doesn’t hold, means  AB = AC ? B = C

 

    vi) Matrix multiplication A x A is represented by A2. Thus, A?A?A?A……...n times = An.

 

    vii) if A is m x n matrix then, .

-

 

 

\mathbf{A} \cdot \mathbf{B}=\left[\begin{array}{cc}{-4} & {3} \\ {5} & {-4}\end{array}\right] \cdot\left[\begin{array}{cc}{4} & {3} \\ {5} & {4}\end{array}\right]=\left[\begin{array}{cc}{-1} & {\;\;\;0} \\ {\;\;\;0} & {-1}\end{array}\right]=-\text{I}

hence option B is correct.

 

Posted by

Pankaj Sanodiya

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions