List of top Mathematics Questions on matrix transformation

If \(å= î+2ĵ + k, b = 3(î - ĵ + k), å · c = 3\) and \(å \times č = b\), then \(å·((xb)-b-č)\)=
If \( A = \begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix} \), then \( A^{-1} \) is:
If \( B = \begin{bmatrix} 3 & a & -1 \\ 1 & 3 & 1 \\ -1 & 1 & 3 \end{bmatrix} \) is the adjoint of a \( 3 \times 3 \) matrix \( A \) and \( |A| = 4 \), then \( a \) is equal to:
Let $A = \begin{bmatrix} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{bmatrix}, a , b \in R$. 
If for some $n \in N , A ^{ n }=\begin{bmatrix}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{bmatrix}$ 
then $n + a + b$ is equal to _________.

Let $A=\begin{pmatrix}1 & 0 & 0 \\ 0 & 4 & -1 \\ 0 & 12 & -3\end{pmatrix}$ Then the sum of the diagonal elements of the matrix $(A+I)^{11}$ is equal to :

If $A$ and $B$ are two non-zero $n \times n$ matrics such that $A ^2+ B = A ^2 B$, then
Let $\lambda \in R$ and let the equation $E$ be $|x|^2-2|x|+|\lambda-3|=0$. Then the largest element in the set $S=$ $\{x+\lambda: x$ is an integer solution of $E\}$ is

If \(A=\frac{1}{2}\begin{bmatrix}1 & \sqrt{3} \\ -\sqrt{3} & 1\end{bmatrix}\), then :

Let \(A=\) [\(a_{ij}\)]\(_{2\times2}\) be a matrix and \(A^2 = I\) where \(a_{ij} \neq0\). If a sum of diagonal elements and b=det(A), then \(3a^2+4b^2\) is

Let A =\(\left[\begin{matrix} 2 & 1 & 0 \\   1 & 2 & -1 \\   0 & -1 & 2  \end{matrix} \right]\). If |adj(adj(adj 2A)) | = (16)n, then n is equal to

If \( A = \begin{bmatrix} 1 & 5 \\ \lambda & 10 \end{bmatrix} \), \( A^{-1} = \alpha A + \beta I \) and \( \alpha + \beta = -2 \), then \( 4\alpha^2 + \beta^2 + \lambda^2 \) is equal to:

Let P = \(\left[\begin{matrix}   \frac{\sqrt3}{2} & \frac{1}{2} \\   -\frac{1}{2} & \frac{\sqrt3}{2}  \end{matrix}\right]\) A = \(\left[\begin{matrix}   1 & 1 \\   0 & 1  \end{matrix}\right]\) and Q = PAPT. If PTQ2007P = \(\left[\begin{matrix}   a & b \\   c & d  \end{matrix}\right]\), then 2a+b-3c-4d equal to

\(\begin{array}{l} \text{Consider a matrix}~A=\begin{bmatrix}\alpha & \beta & \gamma \\\alpha^2 & \beta^2 & \gamma^2 \\\beta+\gamma & \gamma+\alpha & \alpha+\beta \\\end{bmatrix}\end{array}\)
where \(α, β, γ\) are three distinct natural numbers.
If \(\begin{array}{l}\frac{\text{det(adj(adj(adj(adj A))))}}{\left(\alpha-\beta\right)^{16}\left(\beta-\gamma\right)^{16}\left(\gamma-\alpha\right)^{16}}=2^{32}\times3^{16},\end{array}\)
then the number of such 3-tuples \((α, β, γ)\) is _________.