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Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 46 Maths Textbook Solution.

Answers (1)

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Answer: $B \: is \: 2\times3$ order matrix

Hint: Here, we use the basic concept of transpose of matrix

Given: $A \: is \: 2\times3$ matrix and $B$ is matrix such that $A^{T}B\: and \: BA^{T}$ both are defined then what is order of $B$

Solution:

$A \: is \: 2\times3$ matrix

So,

$A^{T}$ is $3\times 2$ matrix

Here, $A^{T}B$ is exist

$=A^{T} _{3\times2}\: B_{m\times n}$

So, $m=2$ in $B$

Here $BA^{T}$ is exist

$=B_{2\times n}\: A^{T}_{3\times 2}$

So, $n=3$ in $B$

So, $B$ is $2\times3$ matrix

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