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  • Which of the following statements are True or False If (AB)’ = B’A’, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

Which of the following statements are True or False
If (AB)’ = B’A’, where A and B are not square matrices, then number of rows in A is equal to number of columns in B and number of columns in A is equal to number of rows in B.

Answers (1)

True

If A and B are any two matrices for which AB is defined, and (AB)’=B’A’.

$A is of order $m \times n$ and $B$ is of order $p \times q\\ (A B)^{\prime}=B^{\prime} A^{\prime} \\ \left.A_{(m \times n)} B_{(p \times q)}\right. \text { defined if } \Rightarrow n=p

A B$ is of order $m \times q$

(A B)^{\prime}$ is of order $q \times m$

$B' is order of $q \times p

A^{\prime}$ is of order $n \times m$ $

B^{\prime} A^{\prime}$ is defined if $\Rightarrow p=n$

B'A'$ is of order $q \times m$

Hence given statement is true.

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