Matrices

Let $I$be an identity matrix of order $2\times\,2$and$P=\left[\begin{matrix} 2 & -1 \\ 5 & -3 \end{matrix}\right]$. Then the value of $n\in\,N$ forwhich $P^{n}=5I-8P$ is equal to ___ .

If for the matrix, $A=\left[\begin{matrix} 1 & -\alpha\, \\ \alpha\, & \beta\, \end{matrix}\right],AA^{T}=I_{2}$,then the value of $\alpha\,^{4}+\beta\,^{4}$ is :

Let$A+2B=\left[\begin{matrix} 1 & 2 & 0 \\ 6 & -3 & 3 \\ -5 & 3 & 1 \end{matrix}\right]$and$2A-B=\left[\begin{matrix} 2 & -1 & 5 \\ 2 & -1 & 6 \\ 0 & 1 & 2 \end{matrix}\right].$If$Tr\left(A\right)$denotes thesum of all…

If $A$is a$3\times\,3$matrix and$\left|A\right|=2$, then$\left|3\operatorname{adj}\,\left(\left|3A\right|A^{2}\right)\right|$is equal to

Consider the following statements in respect of a skew-symmetric matrix A of order 3: All diagonal elements are zero. The sum of all the diagonal elements of the matrix is zero. A is orthogonal matrix. Which of the…

If P is a skew-symmetric matrix of order 3 , then what is $\operatorname{det}(\mathrm{P})$ equal to?

If $f(\theta) = \begin{pmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{pmatrix}$, then what is $\{f(\pi)\}^2$ equal to?

What is the order of the product $\left[\begin{array}{lll} x & y & z \end{array}\right]\left[\begin{array}{lll} a & h & g \\ h & b & f \\ g & f & c \end{array}\right]\left[\begin{array}{l} x \\ y \\ z \end{array}\right]…

Consider the following statements: Every zero matrix is a square matrix. A matrix has a numerical value. A unit matrix is a diagonal matrix. Which of the above statements is/are correct?

The determinant of an orthogonal matrix is

If a matrix A has inverses B and C , then which one of the following is correct?

If $A$ is a square matrix of order 3 with $|\mathrm{A}| \neq 0$, then which one of the following is correct?