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Question
If A is 2 × 3 matrix and B is a matrix such that AT B and BAT both are defined, then what is the order of B ?
Solution
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`
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