List of top Mathematics Questions on Matrix asked in COMEDK UGET

If \( A(t) = \begin{pmatrix} \cos t & \sin t \\ -\sin t & \cos t \end{pmatrix} \), then the product of \( A(t) \) and \( A(-t) \) is
If \( 2A + 3B = \begin{bmatrix} 2 & -1 & 4 \\ 3 & 2 & 5 \end{bmatrix} \) and \( A + 2B = \begin{bmatrix} 5 & 0 & 3 \\ 1 & 6 & 2 \end{bmatrix} \), then \( B = \)
If \( A = \left( \begin{matrix} 1 & 2 \\ 0 & 1 \end{matrix} \right), \, P = \left( \begin{matrix} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{matrix} \right), \, Q = P^T A P \), then \( PQ^{2014} \) is:

If $$ A = \begin{pmatrix} k + 1 & 2 \\4 & k - 1 \end{pmatrix}$$ is a singular matrix, then possible values of k are

If $ A \text{ is a matrix of order 4 such that } A(\text{adj } A) = 10 I, \text{ then } |\text{adj } A| \text{ is equal to} $

If $ A = \begin{bmatrix} 2 & 2 \\3 & 4 \end{bmatrix}, \quad \text{then} \quad A^{-1} \text{ equals to} $

If A ⋅ adj(A) = [ -2 0 0 ]
[ 0 -2 0 ]
[ 0 0 -2 ], then |adj(A)| equals: