Question

If $A=\left[\begin{array}{cc}3& 4\\ 5& 6\\ 7& 8\end{array}\right]$ and $B=\left[\begin{array}{ccc}3& 5& 7\\ 4& 6& 8\end{array}\right]$, then which one of the following is correct?

• A. $B$ is the inverse of $A$
• B. $B$ is the adjoint of $A$
• C. $B$ is the transpose of $A$
• D. None of the above.

Answer 1

The correct option is C $B$ is the transpose of $A$

A is not a square matrix , so inverse and adjoint is not defined for A.
$A=\left[\begin{array}{cc}3& 4\\ 5& 6\\ 7& 8\end{array}\right]$

$A^T=\left[\begin{array}{ccc}3& 5& 7\\ 4& 6& 8\end{array}\right]=B$

$\therefore B$ is the transpose of $A$.

Hence, option C is correct