List of top Mathematics Questions on Transpose of a Matrix

Let $ A = [a_{ij}] $ be a $ 2 \times 2 $ matrix whose elements are given by $ a_{ij} = \frac{(i + 2j)^2}{3} $. Then $ A^{\prime} $ is given by :

If $ A = \begin{bmatrix} \cos x & -\sin x \\ \sin x & \cos x \end{bmatrix} $ and $ A + A^{\prime} = I $, then the value of $ x \in \left[ 0, \dfrac{\pi}{2} \right] $ is

If A and B are symmetric matrices of same order such that $\text{AB} + \text{BA} = \text{X}$ and $\text{AB} - \text{BA} = \text{Y}$, then $(\text{XY})^\text{T} =$

If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha\\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $\alpha \in (\frac{\pi}{2}, \frac{3\pi}{2})$. If $A + A^T = I$, then $\alpha =$}

If $A = \begin{bmatrix} \sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha \end{bmatrix}$ and $\alpha \in (\frac{\pi}{2}, \frac{3\pi}{2})$, if $A + A^T = I$, then $\alpha =$}

Let $A=\begin{pmatrix}1 & 3 & 5 \\ -6 & 8 & 3 \\ -4 & 6 & 5\end{pmatrix}$ and $P=\frac{1}{2}(A + A^T)$. Then:

If \[ A = \begin{bmatrix} 0 & -1 & 2 1 & 0 & 3 -2 & -3 & 0 \end{bmatrix} \] then $ A + 2A^T = $

The inverse of the matrix \[ \begin{bmatrix} 1 & 0 & 0 \\ 3 & 3 & 3 \\ 5 & 2 & -1 \end{bmatrix} \] is:

The negative of $ (p \land (\sim q)) \lor (\sim p) $ is equivalent to:

If \[ B = \begin{bmatrix} 3 & \alpha & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3 \end{bmatrix} \] is the adjoint of a 3x3 matrix $ A $ and $ |A| = 4 $, then $ \alpha $ is equal to:

If $ A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} $, then $ A^{-1} $ is:

The variance of the following probability distribution is:

\[ \begin{array}{|c|c|} \hline x & P(X) \\ \hline 0 & \frac{9}{16} \\ 1 & \frac{3}{8} \\ 2 & \frac{1}{16} \\ \hline \end{array} \]

The converse of $ ((\sim p) \land q) \Rightarrow r $ is:

Let D_k=$\begin{vmatrix} 1 & 2k & 2k-1\\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2 \end{vmatrix} $ If $∑^n_{k=1} D_k=96,$ The n is equal to

Let $P$ be a square matrix such that $P^2 = I - P$. For $\alpha, \beta, \gamma, \delta \in \mathbb{N}$, if $P^\alpha + P^\beta = \gamma I - 29P$ and $P^\alpha - P^\beta = \delta I - 13P$, then $\alpha + \beta + \gamma - \delta$ is equal to:

If $ A = \begin{bmatrix} 2 & -1 \\ -7 & 4 \end{bmatrix} $ and $ B = \begin{bmatrix} 4 & 1 \\ 7 & 2 \end{bmatrix} $, then $ B^T A^T $ is:

Let B =$\begin{bmatrix} 1 & 3 & α \\ 1 & 2& 3 \\ α & α & 4 \end{bmatrix}$ , α>2 be the adjoint of a matrix A and |A| = 2, then [α - 2α α] B$\begin{bmatrix} α \\ -2α \\ α \end{bmatrix}$is equal to

Let A=$\begin{bmatrix} 1 & \frac{1}{51} \\ 0 & 1\end{bmatrix}$. If B=$\begin{bmatrix} 1 & 2 \\ -1 & -1\end{bmatrix}$A $\begin{bmatrix} -1 & -2 \\ 1 & 1\end{bmatrix}$, then the sum of all the elements of the matrix $\sum^{50}_{n=1}B^n$ is equal to

let $A=\begin{bmatrix} 1 & \frac{1}{51} \\ 0& 1 \end{bmatrix}$ if $B=\begin{bmatrix} 1 &2\\ -1& -1 \end{bmatrix} A=\begin{bmatrix} -1 &2\\ 1& 1 \end{bmatrix}$ then the sum of all the elements of the matrix $∑ ^{50}_{n=1}$ Bⁿ is Equal to

if A=$\frac{1}{5! 6! 7!}\begin{bmatrix} 5! & 6! & 7!\\ 6! & 7! & 8! \\ 7! & 8! & 9! \end{bmatrix}$, then |adj(adj(2A))| is equal t

If $ A $ is an $ n \times n $ non-singular matrix such that $ AA^T = A^{-1}A $ and $ B = A^{-1}A^T $, then $ BB' $ is equal to

Let A = [a_ij] be a square matrix of order 3 such that a_ij = 2^j^–ⁱ, for all i, j = 1, 2, 3. Then, the matrix A² + A³ + … + A¹⁰ is equal to

Let A be a $3×3$ real matrix such that $A\begin{pmatrix} 1 \\1 \\ 0 \end{pmatrix}$=$\begin{pmatrix} 1 \\1 \\ 0 \end{pmatrix}$; $A\begin{pmatrix} 1 \\0 \\ 1 \end{pmatrix}$=$A\begin{pmatrix} -1 \\0 \\ 1 \end{pmatrix}$ and $A\begin{pmatrix} 0 \\0 \\ 1 \end{pmatrix}$=$\begin{pmatrix} 1 \\1 \\ 2 \end{pmatrix}$
If $X = [x_1, x_2, x_3]^T $and $I$ is an identity matrix of order $3$, then the system $[A−2I]X $= $\begin{pmatrix} 4 \\1 \\ 1 \end{pmatrix}$ has:

If $ A $ and $ B $ are square matrices of same order and $ A = A^T, B = B^T $, then $ (ABA)^T = $

Let

A = (\begin{array}{ccc} 0 & 2 q & r \\ p & q & - r \\ p & - q & r \end{array})

. If

A A^{T} = I_{3}

, then

| p |

is: