List of top Mathematics Questions on Invertible Matrices asked in BITSAT

If \( A = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \), \( P = \begin{pmatrix} 1 & 1 \\ 0 & 1 \end{pmatrix} \) and \( X = A P A^T \), then \( A^T X^{50} A = \) 
 

If matrix
\[ A = \begin{bmatrix} 3 & -2 & 4 \\ 1 & 2 & -1 \\ 0 & 1 & 1 \end{bmatrix}, \quad \text{and} \quad A^{-1} = \frac{1}{k} \, \text{adj}(A), \]
then \(k\) is:
If $A = \begin{bmatrix}1&1\\ 1&1\end{bmatrix}$ then $A^{100}$ :
If $a.b = a.c$ and $a \times b = a \times c$, then correct statement is