List of top Mathematics Questions on Matrices and Determinants asked in Bihar Board XII

If \( A = \left[ \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right] \), find \( A^{100} \).
If \( A = [1 \ 2 \ 3] \), find \( A' \).
If \[ A = \begin{bmatrix} 2 & -2 & -4 \\ -1 & 3 & 4 \\ 1 & -2 & -3 \end{bmatrix}, \] show that \( A^2 = A \).
Evaluate the following matrix multiplication: \[ \begin{pmatrix} -3 & 5 & 2 \end{pmatrix} \times \begin{pmatrix} 1 \\ 6 \\ -4 \end{pmatrix} \]
Let \( A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \). Then, \( A^5 = \):
If \( A = \begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix} \), then \( \text{adjoint } A = \):
The matrix \( A = [a_{ij}] \) of size \( m \times n \) is a square matrix if:
If \[ A = \begin{bmatrix} 2 & -3 \\ 4 & 6 \end{bmatrix} \] then \[ A^{-1} = \] The correct answer is:
If \[ A = \begin{bmatrix} 3 & 6 \\ -5 & 4 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 7 & 8 \\ 5 & 6 \end{bmatrix}, \] then \[ 6A - 5B = \] The correct answer is:
If \[ A = \begin{bmatrix} 2 & \sqrt{2} & 0 \\ 3 & -2 & \frac{2}{5} \end{bmatrix} \] then \[ A^t = \] The correct answer is:
If \[ 2A + B + X = 0 \] where \[ A = \begin{bmatrix} -1 & 2 \\ 3 & 4 \end{bmatrix} \quad \text{and} \quad B = \begin{bmatrix} 3 & 1 \\ 5 & -2 \end{bmatrix}, \] then \[ X = \]