Class 12 Mathematics questions for CBSE

For the matrix \[ A = \begin{bmatrix} 2 & 3 \\ 1 & 4 \end{bmatrix} \], find the determinant. What does it imply about the matrix?

If A is a 2x2 matrix with elements \[ a, b, c, d \], what is the adjoint of A?

Calculate the determinant of the following matrix: \[ \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \]

Given a matrix A, if the adjoint of A is denoted as adj(A), what is the relationship between A and adj(A) if A is invertible?

If the determinant of a matrix A is 5, what is the determinant of the matrix 2A?