Question

If ${(A+B^T)}^T$ is a matrix of order $4\times 3$ then the order of matrix B is

• A. $3\times 4$
• B. $4\times 3$
• C. $3\times 3$
• D. $4\times 4$

Answer 1

The correct option is B $4\times 3$

If ${(A+B^T)}^T$ is of the order $4\times 3$, then $A+B^T$ will be of the order $3\times 4$
Since the sum matrix is always of the order of the addends matrices, both $A$ and $B^T$ will be of the order $3\times 4$
And when $B^T$ is of the order $3\times 4$ then $B$ will be of the order $4\times 3$