Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If A is a matrix of an order mxn and B is a matrix of an order pxq then which of the following statement is always true for their multiplicationOption: 1</strong

If A is a matrix of an order mxn and B is a matrix of an order pxq then which of the following statement is always true for their multiplication

Option: 1

p=n


Option: 2

Order of matrix AxB is mxq


Option: 3

If A and B are equal matrices than boh the matrix is a square matrix.


Option: 4

All of the above


Answers (1)

best_answer

 

 

Multiplication of two matrices -

Matrix multiplication: 

Two matrices  A and B are conformable for the product AB if the number of columns in A and the number of rows in B is equal. Otherwise, these two matrices will be non-conformable for matrix multiplication. So on that basis,

i) AB is defined only if col(A) = row(B)

ii) BA is defined only if col(B) = row(A)

 

-

 

 

option (a) is true 

let \\A=\left[\begin{array}{lll}{a_{11}} & {a_{12}} & {a_{13}}\end{array}\right]_{1\times3}\;\;\text{and}\;\;B=\left[\begin{array}{l}{b_{11}} \\ {b_{21}} \\ {b_{31}}\end{array}\right]_{3\times1}

then,

\\A\times B=\left[\begin{array}{lll}{a_{11}} & {a_{12}} & {a_{13}}\end{array}\right]\left[\begin{array}{l}{b_{11}} \\ {b_{21}} \\ {b_{31}}\end{array}\right]\\=[\mathrm{a}_{11} \cdot \mathrm{b}_{11}+\mathrm{a}_{12} \cdot \mathrm{b}_{21}+\mathrm{a}_{13} \cdot \mathrm{b}_{31}]_{1\times 1}

hence the order of matrix AxB is mxq.

therefore, option b is also true

If A and B are equal matrices than m=p and n=r

for AxB n=p 

but m=p (both are equal matrix)

hence, m=n 

or matrices A and B are a square matrices

option (c) is also correct

 

All of the above is correct

Posted by

HARSH KANKARIA

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions