List of top Mathematics Questions on Matrices asked in AIEEE

If $\omega \ne 1$ is the complex cube root of unity and matrix $ H =\begin{bmatrix}\omega&0\\ 0&\omega\end{bmatrix}$, then $H^{70}$ is equal to -

The number of $3 \times 3$ non-singular matrices, with four entries as $ 1 $ and all other entries as $0$, is

If $A$ and fl are square matrices of size $n \times n$ such that $A^{2}-B^{2}=\left(A-B\right)\left(A+B\right)$, then which of the following will be always true ?

Let $A=\begin{pmatrix} 1&-1 &1 \\[0.3em] 2 &1 &-3 \\[0.3em] 1 &1&1 \end{pmatrix}$ and $\,10\,B=\begin{pmatrix} 4&2 &2 \\[0.3em] -5 &0 & \alpha \\[0.3em] 1 &-2&3 \end{pmatrix} $. If B is the inverse of A , then $\alpha$ is

If $A = \begin{bmatrix}a&b\\ b&a\end{bmatrix}$ and $A^{2}\begin{bmatrix}\alpha&\beta \\ \beta&\alpha\end{bmatrix}$, then