List of top Mathematics Questions on Matrix Operations asked in KEAM

Let $A = \begin{bmatrix} 2 & x \\ 3 & 1 \end{bmatrix}, B = \begin{bmatrix} 3 & 2 \\ 1 & 4 \end{bmatrix}$ and $C = \begin{bmatrix} 3x+2 & 10 \\ 14-x & 10 \end{bmatrix}$. If $B^T A^T = C$, then the value of $x$ is equal to

Let $A=\begin{pmatrix}0& 2\\ 3& 4\end{pmatrix}$ and $I=\begin{pmatrix}1& 0\\ 0& 1\end{pmatrix}$. If $(I+A)\begin{pmatrix}4&-3\\ 2&-1\end{pmatrix}=\begin{pmatrix}8&-5\\ 22& x\end{pmatrix}$, then the value of $x$ is equal to ________.

Let $A$ be $3 \times 3$, $B$ be $3 \times 2$ and $C$ be $3 \times 1$. Which one of the following products is not defined? ________.