The matrix which is both symmetric and skew-symmetric, is a:

Let A = [aᵢⱼ]ₙₓₙ and B = [bᵢⱼ]ₙₓₙ. Then which of the following is/are true?

(A) AB = BA

(B) (AB)⁻¹ = B⁻¹ A⁻¹

(C) $(AB)^T = B^T A^T$

(D) AB = 0 ⇒ A = 0 or B = 0

Choose the correct answer from the options given below:

If A is a square matrix such that $A^2 = I$, then $(A+I)^3 + (A-I)^3 - 7A$ is equal to

If $A=\begin{bmatrix}2 & 3\\1 & 2\end{bmatrix}, I=\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}$ and $A^2=\alpha A+\beta I$, for some constant $\alpha$ and $\beta$ then the value of $\alpha$ and $\beta$ respectively:

The value of $\begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \end{vmatrix}$ is:

The value of $2y - 3x$, if $2\begin{bmatrix} x & 5 \\ 7 & y-3 \end{bmatrix} + \begin{bmatrix} 3 & -4 \\ 1 & 2 \end{bmatrix} = \begin{bmatrix} 7 & 6 \\ 15 & 14 \end{bmatrix}$ is :

If $A=\begin{bmatrix}0 & b-a & c-a\\a-b & 0 & c-b\\a-c & b-c & 0\end{bmatrix}$ then the value of $\lvert A \rvert$ is