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Explain Solution R. D. Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Multiple Choice Questions Question 38 maths Textbook Solution.

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Answer: m\times n

Given: If A is a matrix of order m\times n and B is the matrix such that AB^{T}and B^{T}A are both defined. Then the order of the matrix B is

Hint: compare order of matrices


Order of the matrix A=m \times n

Order of the matrix B=p \times q

Order of the matrix B^{T}=q \times p

We are given AB^{T} exists

Number of columns in A= Number of rows in B^{T}


Also we are given B^{T}A exists

Number of columns in B^{T}= Number of rows in A


\thereforeOrder of B becomes m\times n

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