List of top Mathematics Questions on matrix transformation asked in JEE Main

If $å= î+2ĵ + k, b = 3(î - ĵ + k), å · c = 3$ and $å \times č = b$, then $å·((xb)-b-č)$=

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 = PAP^T. If P^TQ²⁰⁰⁷P = $\left[\begin{matrix} a & b \\ c & d \end{matrix}\right]$, 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 _________.