List of top Mathematics Questions on types of matrices

If \( A = \begin{vmatrix} 1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2 \\ \end{vmatrix} \), then the value of \( A \) is:

If R(t)= beginpmatrix cos t & sin t
-sin t & cos t endpmatrix, then R(s)R(t) equals

If
\[ A = \frac{1}{3} \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix} \] is an orthogonal matrix, then:

If
\[ R(t) = \begin{pmatrix} \cos t & \sin t \\ -\sin t & \cos t \end{pmatrix}, \]
then \(R(s)R(t)\) equals

If \(\begin{bmatrix} \alpha & \beta \\ \gamma & -\alpha \end{bmatrix}\) is a square root of identity matrix of order 2, then

Let \( A = \begin{bmatrix} 0 & \alpha \\ 0 & 0 \end{bmatrix} \) and \( (A + I)^5 - 50A = \begin{bmatrix} a & b \\ c & d \end{bmatrix} \). Find \( abc + abd + bcd + acd \):

If A=bmatrix1&3
3&2
2&5bmatrix and B=bmatrix-1&-2
0&5
3&1bmatrix and A+B-D=0 (zero matrix), then D matrix will be