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 $A$ be a square matrix and $A^{T}$ be its transpose. Which one of the following is true?

The value of the determinant $\begin{vmatrix}(10^{5}+10^{-5})^{2}&(10^{5}-10^{-5})^{2}& 1\\ (100^{5}+100^{-5})^{2}&(100^{5}-100^{-5})^{2}& 1\\ (6^{100}+6^{-100})^{2}&(6^{100}-6^{-100})^{2}& 1\end{vmatrix}$ is equal to

Let $A=\begin{pmatrix}1&\tan x\\ -\tan x& 1\end{pmatrix}.$ Then $AA^{T}$ is equal to

If $\begin{vmatrix} x + 2 & 8 & 9 \\ 4 & x + 6 & 9 \\ 4 & 8 & x + 7 \end{vmatrix} = (x - 2)^{2}(ax + b),$ then the values of $a$ and $b$ respectively are

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? ________.

If $ A $ is a $ 3 \times 3 $ matrix and $ |B| = 3|A| $ and $ |A| = 5 $, then find $ \left| \frac{\text{adj} B}{|A|} \right| $.

If $ X = A \times B $, $ A = \begin{bmatrix} 1 & 2 \\-1 & 1 \end{bmatrix} $, $ B = \begin{bmatrix} 3 & 6 \\5 & 7 \end{bmatrix} $, find $ x_1 + x_2 $.