The inverse of the matrix $\begin{bmatrix} 4 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 6 \end{bmatrix}$ is

Let A = $[a_{ij}]_{n \times n}$ be a matrix. Then

Match List-I with List-II

Choose the correct answer from the options given below:

Given a matrix A of order 3x3. If |A|=3 then the value of |A(adj A)| is:

With reference to the matrix $A=\begin{bmatrix}5&0&0\\0&5&0\\0&0&-5\end{bmatrix}$, which of the following are TRUE ?

A. |A|=125

B. A is a scalar matrix.

C. A is a diagonal matrix.

D. |A|=-125

Choose the correct answer from the options given below:

If A is a square matrix $\begin{bmatrix} 5 & -5 \\ -5 & 5 \end{bmatrix}$ such that $A^2 = p\,A$, then the value of p is,

For any 3 ×3 matrix $A$, if $A(adj\,A) = \begin{bmatrix} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{bmatrix}$, then $2|A|$ is equal to

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