List of top Mathematics Questions on Adjoint of a Matrix

If \[ A(\operatorname{adj}A)= \begin{bmatrix} 2026 & 0 & 0\\ 0 & 2026 & 0\\ 0 & 0 & 2026 \end{bmatrix}, \] then the value of \[ \left|\operatorname{adj}A\right| \] is equal to \[ \_\_\_\_. \]

If \( A = \begin{bmatrix} 1 & 2 & -1 \\ -1 & 1 & 2 \\ 2 & -1 & 1 \end{bmatrix} \) then \( |adj(adj A)| \) is equal to

Find the adjoint of \[ A= \begin{pmatrix} 1& 2\\ 3& 4 \end{pmatrix} \]

Consider a \(3\times3\) matrix \(A\). If \[ \operatorname{adj}(A)= \begin{pmatrix} 2& 0& 0\\ 0& 2& 0\\ 0& 0& 2 \end{pmatrix} \] find \(\det(A)\).

If \( B \) is a non-singular \(4\times4\) matrix and \( A \) is its adjoint such that \( |A|=125 \), then \( |B| \) is:

Find the adjoint of the matrix: \[ \left[ \begin{matrix} 2 & 3 \\ 5 & 4 \end{matrix} \right] \]

For a square matrix } A_{n \times n}:
(A) \( |\text{adj } A| = |A|^{n-1} \) 
(B) \( |A| = |\text{adj } A|^{n-1} \) 
(C) \( A (\text{adj } A) = |A| \) 
(D) \( |A^{-1}| = \frac{1}{|A|} \) 
$\text{Choose the \textbf{correct} answer from the options given below:}$

The characteristic equation of a matrix A is λ³ - 5λ² - 3λ + 2I = 0 then |adj A| =