The values of $\lambda$ for which the system of equation $x + 2y + z = 14, - x + y + z = 10, x + \lambda y + z = 2$ has unique solution is

If $A = [a_{ij}]_{3×3}$ where $a_{ij} = \begin{cases} (-1)^{i+j} - 1, & i = j \\ (-1)^{i+j}, & i \neq j \end{cases}$ then the value of $A + A^T$ is:

For a square matrix $A = \begin{bmatrix} 2 & 1 & 3 \\ 0 & -1 & 4 \\ 1 & 2 & 0 \end{bmatrix}$, which of the following statements is/are TRUE ?

A. det (A) = 9.

B. $A_{21}.A_{33} = -12$, where $A_{ij}$ is the cofactor of $a_{ij}$

C. det (A) = $a_{11}A_{11} + a_{12}A_{12} + a_{13}A_{31}$.

D. $\lvert AA'\rvert \neq \lvert A\rvert^2$

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Match List - I with List - II.

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If $\begin{bmatrix} 2x-1 & -3 & 6 \\ 3 & 3y-2 & 4 \\ -6 & -4 & 4z-3 \end{bmatrix}$ is skew symmetric matrix, then $xyz$ is equal to

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

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If $A = \begin{bmatrix} 4 & -1 & \lambda \\ 2 & 0 & 6 \\ 1 & -2 & 7 \end{bmatrix}$, then $\frac{1}{2}A^{-1}$ exist if