If $A(\operatorname{adj} A)=5 I$ where $I$ is the identity matrix of order $3$,then $|\operatorname{adj} A|$ is equal to

The inverse of the matrix $\begin{bmatrix} 5 & -2 \\ 3 & 1 \end{bmatrix}$ is

The inverse of the matrix $A = \begin{bmatrix} 3 & -2 \\ 1 & 4 \end{bmatrix}$ is:

Let $A = \begin{bmatrix} 1 & -2 & 1 \\ -2 & 3 & 1 \\ 1 & 1 & 5 \end{bmatrix}$. Verify that $[adj A]^{-1} = adj(A^{-1})$.

If $\operatorname{adj}\begin{bmatrix} 1 & 0 & 2 \\ -1 & 1 & -2 \\ 0 & 2 & 1 \end{bmatrix} = \begin{bmatrix} 5 & a & -2 \\ 1 & 1 & 0 \\ -2 & -2 & b \end{bmatrix}$, then $[a \quad b]$ is equal to

If $X$ is a square matrix of order $3 \times 3$ and $\lambda$ is a scalar,then $adj(\lambda X)$ is equal to