The following system of equations: $x + y - z = 7$ $4x + \lambda y - \lambda z = 3$ $3x + 2y - 4z = 5$ does not possess a solution if the value of $\lambda$ is:

If A and B are skew-symmetric matrices, then which one of the following is NOT true?

If the matrix $\begin{bmatrix} 5 & x^2 \\ 3x-2 & x-1 \end{bmatrix}$ is symmetric, then values of $x$ are :

Let $A = [a_{ij}]$ be a square matrix, where $a_{ij} = \begin{cases} 0, & \text{when } i = j \\ 1, & \text{otherwise} \end{cases}$. If |adj A| = |A|², then which of the following statements are correct?

(A) A is a skew symmetric matrix.

(B) A is a non-singular matrix.

(C) A is a square matrix of order 4.

(D) A is a symmetric matrix.

Choose the correct answer from the options given below:

Given that $[a_{ij}]$ is a square matrix of order n.

Match the LIST-I with LIST-II

Choose the correct answer from the options given below:

Choose the correct answer from the options given below :

If $A = \begin{bmatrix} 1 & 2 & 3 \\ -4 & -5 & -2 \end{bmatrix}$, $B = \begin{bmatrix} 2 & -3 \\ 4 & -5 \\ 2 & -1 \end{bmatrix}$ and $BA = [b_{ij}]$, then $(b_{23} - b_{31})$ is equal to