Question

If A is $4\times 5$ matrix, if $A^{T}B$ and $B{A}^T$ are defined then $B=$

• A. $5\times 4$
• B. $4\times 4$
• C. $5\times 5$
• D. $4\times 5$

Answer 1

The correct option is D $4\times 5$

If $A$ matrix has order $4\times 5$, then

$A^T$ will have order $5\times 4$

Condition for multiplication of matrices with orders: $m_1\times n_1,m_2\times n_2$ is $n_1=m_2,m_1=n_2$

Therefore, order of matrix $B=4\times 5$