If matrix $A = \begin{bmatrix} 1 & -1 \\ 1 & 1 \end{bmatrix}$,then:

Let $A = \begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & -\sin t & \cos t \end{bmatrix}$. Let $\lambda_{1}, \lambda_{2}, \lambda_{3}$ be the roots of $\det(A - \lambda I_{3}) = 0$, where $I_{3}$ denotes the identity matrix. If $\lambda_{1} + \lambda_{2} + \lambda_{3} = \sqrt{2} + 1$, then the set of possible values of $t$ for $-\pi \leq t < \pi$ is:

If $A$ is a skew-symmetric matrix and $n$ is a positive integer,then $A^n$ is

Consider a matrix $A = \begin{bmatrix} \alpha & \beta & \gamma \\ \alpha^{2} & \beta^{2} & \gamma^{2} \\ \beta+\gamma & \gamma+\alpha & \alpha+\beta \end{bmatrix}$,where $\alpha, \beta, \gamma$ are three distinct natural numbers. If $\frac{\operatorname{det}(\operatorname{adj}(\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A))))}{(\alpha-\beta)^{16}(\beta-\gamma)^{16}(\gamma-\alpha)^{16}}=2^{32} \times 3^{16}$,then the number of such $3$-tuples $(\alpha, \beta, \gamma)$ is $.....$

$A$ and $B$ are two square matrices such that $A^2B = BA$. If $(AB)^{10} = A^K B^{10}$,then $k$ is:

If $A$ and $B$ are $3 \times 3$ matrices and $|A| \neq 0$,then which of the following are true?