Let $A = \begin{bmatrix} 1 & -2 & 3 \\ 1 & 2 & 1 \\ \lambda & 2 & -3 \end{bmatrix}$. If $A^{-1}$ does not exist, then $\lambda =$

For the matrix $A = \begin{bmatrix} 2 & -1 & -1 \\ 0 & 2 & 3 \\ 1 & -2 & 1 \end{bmatrix}$, which of the following statements are correct?

(A) The order of the matrix is 3 × 3

(B) |A| = 21

(C) $|adj\ A| = 225$

(D) A is skew symmetric matrix

Choose the correct answer from the options given below:

if $A = \begin{bmatrix}1 & 0\\3 & 1\end{bmatrix}$ and $A^4 = \begin{bmatrix}1 & 0\\k & 1\end{bmatrix}$ then value of $k$ is

Which of the following statements is incorrect?

If $\begin{bmatrix} 1 & 2 & 1\end{bmatrix}$ $\begin{bmatrix}1 & 2 & 0 \\ 2 & 0 & 1 \\ 1 & 0 & 2 \end{bmatrix} \begin{bmatrix} 0 \\ 2 \\ x\end{bmatrix} = 0,$then value of x is

If a matrix $A = \begin{bmatrix} x+3 & 3 \\ 2x+1 & 5 \end{bmatrix}$ is singular , then the value of $x$ will be

If $A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}$ and $B = \begin{bmatrix} 0 & 2 \\ 2 & 0 \end{bmatrix}$, then the matrix AB is equal to