The matrix $\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{array}\right]$ is a :

(A) scalar matrix

(B) diagonal matrix

(C) skew-symmetric matix

(D) symmetric matrix

Choose the correct answer from the options given below :

For a square matrix $A_{n \times n}$

(A) $|\operatorname{adj} \mathrm{A}|=|\mathrm{A}|^{\mathrm{n}-1}$

(B) $|\mathrm{A}|=|\operatorname{adj} \mathrm{A}|^{\mathrm{n}-1}$

(C) $\mathrm{A}(\operatorname{adj} \mathrm{A})=|\mathrm{A}|$

(D) $\left|\mathrm{A}^{-1}\right|=\frac{1}{|\mathrm{~A}|}$

Let P be a matrix such that $P = \begin{bmatrix} 1 & -1 \\ 0 & 3 \end{bmatrix}$, then which of the following statements are True?

A. P is a symmetric matrix

B. P is not a skew-symmetric matrix

C. The determinant of P is non-zero

D. P is an invertible matrix

Choose the correct answer from the options given below:

The length ($x$) and breadth ($y$) of plot satisfy equations:

If A and B are square matrices of the same order, then (A+B) (A-B) is equal to

If the matrix $\begin{bmatrix} 0 & 7 & -12 \\ -7 & 0 & -5 \\ 2a & 5 & 3b \end{bmatrix}$ is skew-symmetric, then the value of $(4a + 3b)$ is:

If the matrix $A = \begin{bmatrix} \cos\theta & \sin\theta \\ -\sin\theta & \cos\theta \end{bmatrix}$, then $A^2$ is equal to: