With reference to the matrix $A=\begin{bmatrix}5&0&0\\0&5&0\\0&0&-5\end{bmatrix}$, which of the following are TRUE ?

A. |A|=125

B. A is a scalar matrix.

C. A is a diagonal matrix.

D. |A|=-125

Choose the correct answer from the options given below:

If a matrix has 12 elements, then the possible orders it can have, are

(A) 1 × 12

(B) 4 × 3

(C) 6 × 3

(D) 6 × 2

Choose the correct answer from the options given below:

If the matrix $\begin{bmatrix}0 & \alpha & 2\\2 & \beta & 1\\\gamma & -1 & 0\end{bmatrix}$ is skew-symmetric, then $(\beta-\alpha-\gamma)$ equals

If $\begin{bmatrix} 0 & x \\ 2 & 1 \end{bmatrix} + 2\begin{bmatrix} 3 & 1 \\ y & 0 \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 8 & 1 \end{bmatrix}$, then the value of $2x+3y$ is :

If A is a square matrix and I is an identity matrix of same order such that $A^2 = A$, then $(I + A)^3 - 8I$ is equal to

Let A be a square matrix of order 3 such that $|A|=3$, then the value of $\frac{|adj(adjA)|}{|A|}$ is

If $0 < x < \pi$ and the matrix $\begin{bmatrix} 4\sin x & -1 \\ -3 & \sin x \end{bmatrix}$ is singular, then the values of $x$ are :