List of top Mathematics Questions on Adjoint and Inverse of a Matrix

Let \( A \) be a square matrix of order 3 such that \( |A| = 5 \). Find the value of the determinant of its adjoint matrix, \( |\text{adj}(A)| \).

If $A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$, then $\text{adj}(A)$ is:

If A is a square matrix of order 3 and |A|=5, then |adj(adjA)| is:

If A is a square matrix of order 3 such that |A|= 2, then the value of |adj(adj A)| is:

If \(|A|=3\)  and \(A^{-1}=\begin{bmatrix}        3 &-1 \\[0.3em]        \frac{-5}{3} & \frac{2}{3}    \\[0.3em]     \end{bmatrix}\) then adj \(A\) is 

If \(A=\begin{bmatrix} x & 1 \\ 1 & 0 \end{bmatrix}\)and A = A^-1, then the value of x is :

If A = \(\begin{bmatrix}2a & 0& 0\\[0.3em]0& 2a& 0\\[0.3em]0&0 & 2a\\[0.3em] \end{bmatrix}\), then the value of \(|adj A|\)is:

If A is an invertible matrix, such that A² - A + I = 0, then the inverse of A is :

If \(A=\begin{bmatrix} -2&6\\-5&-1\end{bmatrix}\) then \(A^{-1}\) is:

If, A is a square matrix of order 3 and |A| = -2 then. \(|-2 \ A^{-1}|\) is:

If \(\begin{bmatrix}      1 & 3 & 5          \\[0.3em]      1 & 0   &3 \\[0.3em]        0 &1 &0      \end{bmatrix}\),then \(|(adjA)| \) is: