The value/s of '$\lambda$' for which the system of equations

$\lambda x + 3y - z = 1$

$x + 2y + z = 2$

$-\lambda x + y + 2z = -1$

has unique solution is/are:

(where $R$ is set of real numbers)

Let A, B, C, D and E be matrices of order $2 \times n, 3 \times k, 2\times p, n \times 3$ and $p \times k$ respectively. Choose the correct statement(s) from the following?

(A) EB + DB will be defined if $k = 3, p = n$.

(B) EB + DB will be defined if $k = 2, p = 3$.

(C) If n = p = 2, then the order of the matrix $5A^2 - 3C$ is $2 \times 2$.

(D) If n = p, then the order of the matrix $5A^2 - 3C$ is $p \times k$.

Choose the correct answer from the options given below:

If $\det \begin{pmatrix} 2x & 5 \\ 8 & x \end{pmatrix} = \det \begin{pmatrix} 6 & -2 \\ 1 & 1 \end{pmatrix}$, then the value of $x$ is

If $A$ and $B$ are square matrices of the same order, then which of the following statements are correct?

(A) $|A^{-1}| = |A|^{-1}$

(B) $adj(A) = |A|A^{-1}$

(C) $(A + B)^{-1} = B^{-1} + A^{-1}$

(D) $(AB)^{-1} = B^{-1}A^{-1}$

Choose the correct answer from the options given below:

If A is an invertible matrix of order 3 and the determinant of A is 9, then the determinant of $A^{-1}$ is:

Match List - I with List - II.

Choose the correct answer from the options given below :

Let A be a non-singular square matrix of order 3 and $|adj A| = 5$ then $|A|$ is equal to