Question

If A is 2 × 3 matrix and B is a matrix such that A^T B and BA^T both are defined, then what is the order of B ?

Answer 1

Order of A =

`2xx3`

Order of 

`A^T=3xx3`

Let order of B =

``

`Given:  A^T B and B A^T  are defined 

If `A ^T  _( 3 × 2) B _(m×n)`exists, then the number of columns in `A^T` must be equal to number of rows in B.

\[ \Rightarrow m = 2\]

If `B _(m×n) A ^T  _( 3 × 2) `exists, then the number of columns in B must be equal to number of rows in `A^T ` .

\[ \Rightarrow n = 3\]

∴ Order of B =   `  2  × 3`