List of top Mathematics Questions on Matrices asked in AP EAPCET

Let \(A\) be a \(3\times3\) matrix such that \[ AA^{T}=I_3. \] Then \(A\) is:

If \[ A= \begin{bmatrix} \sin\alpha & -\cos\alpha\\ \cos\alpha & \sin\alpha \end{bmatrix} \] and \(A+A^{-1}=I\), then \(\alpha=\)

If \[ A= \begin{bmatrix} 1 & 1 & 3\\ 1 & 7 & 9\\ 2 & 3 & 7 \end{bmatrix} \] then \[ \mathrm{Tr}(A^2-A)= \] is equal to:

If \[ A=\begin{bmatrix} 3 & 4\\ 5 & 6 \end{bmatrix} \] and \[ B=\begin{bmatrix} x & 0\\ 0 & y \end{bmatrix}, \quad x,y\in \mathbb{N}, \] then:

If \(A\) and \(B\) are symmetric matrices of same order such that \[ AB+BA=X \] and \[ AB-BA=Y, \] then \((XY)^T=\)

If the ranks of the matrices \[ A= \begin{bmatrix} 1 & 0 & 1\\ 2 & 1 & 2\\ 1 & 0 & -1 \end{bmatrix} \] and \[ B= \begin{bmatrix} 1 & 2 & 3 & 4\\ 2 & 4 & 6 & -8 \end{bmatrix} \] are \(r_1\) and \(r_2\) respectively, then \(r_1-r_2=\)

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

If \[ A= \begin{bmatrix} 1 & 0 \\ 2 & 1 \end{bmatrix}, \quad B= \begin{bmatrix} 1 & 3 \\ 0 & 1 \end{bmatrix}, \] then \[ \det(A^4+B^6)= \]

If \[ A= \begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix}, \] then \(AA^T\) is a

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 \[ (A^T)^2+(12A)^T= \]