List of top Mathematics Questions on Matrices and Determinants asked in AP EAPCET

If $ A = \begin{bmatrix} -1 & x & -3 \\ 2 & 4 & z \\ y & 5 & -6 \end{bmatrix} $ is symmetric and $ B = \begin{bmatrix} 0 & 2 & q \\ p & 0 & 4 \\ -3 & r & s \end{bmatrix} $ is skew-symmetric, then find $ |A| + |B| - |AB| $

If the inverse of $$ \begin{bmatrix} -x & 14x & 7x \\ 0 & 1 & 0 \\ x & -4x & -2x \end{bmatrix} $$ is $$ \begin{bmatrix} 2 & 0 & 7 \\ 0 & 1 & 0 \\ 1 & -2 & 1 \end{bmatrix} $$ then the value of $$ \begin{vmatrix} x & x+1 & x+2 \\ x+1 & x+2 & x+3 \\ x+2 & x+3 & x+4 \end{vmatrix} $$

Consider the matrices \[ A = \begin{bmatrix} x & y & 0 \\ -3 & 1 & 2 \\ 1 & -2 & z \end{bmatrix}, B = \begin{bmatrix} 1 & -2 & -2 \\ 2 & 0 & 1 \\ 2 & 1 & 0 \end{bmatrix} \] If the cofactors of the elements \( z, 1 \) in 3rd row and \( x \) of \( A \) are 9, 4, 3 respectively, then \( AB = \)

If the cofactors of the elements 3, 7, and 6 of the matrix \( \begin{bmatrix} 1 & 2 & 3 \\ 4 & -1 & 7 \\ 2 & 4 & 6 \end{bmatrix} \) are \( a, b, c \) respectively, then evaluate: \[ \left[ a \ b \ c \right] \begin{bmatrix} 1 \\ 4 \\ 2 \end{bmatrix} + \left[ a \ b \ c \right] \begin{bmatrix} 3 \\ 7 \\ 6 \end{bmatrix} \]

Let \( B = \begin{bmatrix} 2 & 6 & 4 \\ 1 & 0 & 1 \\ -1 & -1 & -1 \end{bmatrix} \), \( C = \begin{bmatrix} -1 & 0 & 1 \\ 1 & 1 & 3 \\ 2 & 0 & 2 \end{bmatrix} \), and if a matrix \( A \) is such that \( BAC = I \), then \( A^{-1} = \)

If \( \det(AB) = \det(A)\det(B) \) and \( A \) is a non-singular matrix of order \( 3 \times 3 \), then \( \det(\text{adj}(A)) \) is:

If \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \), where \( a, b, c, d \in \{-1, 1\} \), then the number of singular matrices in \( A \) is: