List of top Mathematics Questions on Matrices asked in AP EAPCET

If \[ A= \begin{bmatrix} 1 & 0 & 0\\ a & -1 & 0\\ b & c & 1 \end{bmatrix} \] is such that \[ A^2=I, \] then

If \[ A=\begin{bmatrix} 2 & -3\\ -4 & 1 \end{bmatrix}, \] then \[ (A^T)^2+(12A)^T= \]

If \( A = \begin{bmatrix} x & 0 \\ 1 & 1 \end{bmatrix} \) and \( B = \begin{bmatrix} 8 & 0 \\7 & 1 \end{bmatrix} \), and \( A^3 = B \), then \( x = \) ?

If $ AX = D $ represents the system of simultaneous linear equations: $$ \begin{aligned} x + y + z &= 6 \\ 5x - y + 2z &= 3 \\ 2x + y - z &= -5 \end{aligned} $$ Then compute: $ (\text{Adj } A) D $

If \( b \) and \( c \) are non-zero real numbers, and \[ A = \begin{bmatrix} 1 & b & c \\ b & 2 & 3 \\ c & 3 & 4 \end{bmatrix}, \quad B = \begin{bmatrix} 0 & b & c \\ -b & 0 & 2 \\ -c & -2 & 0 \end{bmatrix}, \] then \( \det(A + B) = \) ?

If $a$, $b$, $c$ are respectively the $5^{\text{th}$, $8^{\text{th}}$, $13^{\text{th}}$ terms of an arithmetic progression, then}
$\begin{vmatrix} a & 5 & 1 \\ b & 8 & 1\\ c & 13 & 1 \end{vmatrix} = $

If \( A = \begin{bmatrix} 1 & -2 & 2 \\ -2 & -6 & 5 \\ 0 & 0 & 4 \end{bmatrix} \) then Adj A =

Let \( A = \begin{bmatrix} b^2+c^2 & a^2 & a^2 \\ b^2 & c^2+a^2 & b^2 \\ c^2 & c^2 & a^2+b^2 \end{bmatrix} \). If \(a = \sin \pi/6, b = \cos \pi/4\) and \(c = \cot \pi/2\) then A is

If $$ A = \begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix} $$ then find: $$ \det(A^6 + B^6) $$

If $$ A = \begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix} $$ then $ AA^T $ is:

Let $$ G(x) = \begin{bmatrix} \cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1 \end{bmatrix} $$ If $ x + y = 0 $, then evaluate $ G(x)G(y) $

Given $a_i^2 + b_i^2 + c_i^2 = 1$ and $a_i a_j + b_i b_j + c_i c_j = 0$ for $i \neq j$, and
\[ A = \begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{bmatrix} \] Then $\det(AA^T) = $ ?

If $A = \frac{1}{7} \begin{bmatrix} 3 & -2 & 6 \\-6 & -3 & 2 \\ -2 & 6 & 3 \end{bmatrix}$, then $A^{-1} = $ ?

If $A = \begin{bmatrix} \alpha^2 & 5 \\ 5 & -\alpha \end{bmatrix}$ and $\det(A^{10}) = 1024$, then $\alpha =$ ?

If the rank of the matrix \[ A = \begin{bmatrix} 1 & 2 & 1 & -1 \\ -1 & 2 & 3 & 5 \\ 0 & 1 & k & k \end{bmatrix} \] is 2 and \( k \) is a real number, then \( k \) is a root of which of the following quadratic equations?