List of top Mathematics Questions on Determinants asked in AP EAPCET

Let \[ A= \begin{bmatrix} 1 & 2\\ 2 & 1 \end{bmatrix}. \] Then the determinant of \(A^2\) is:

If \[ A= \begin{bmatrix} 1&2\\ 3&4 \end{bmatrix}, \] then \(\det(A)\) is equal to:

Let \(f,g,h\) be differentiable functions such that \[ \begin{vmatrix} f(x) & g(x) & h(x)\\ f'(x) & g'(x) & h'(x)\\ f''(x) & g''(x) & h''(x) \end{vmatrix} =0. \] Then which of the following statements is correct?

If \(b\) and \(c\) are non-zero real numbers, \[ A= \begin{bmatrix} 1 & b & c\\ b & 2 & 3\\ c & 3 & 4 \end{bmatrix} \quad \text{and} \quad B= \begin{bmatrix} 0 & b & c\\ -b & 0 & 2\\ -c & -2 & 0 \end{bmatrix}, \] then \(\det(A+B)=\)

If \(AX=D\) represents the system of simultaneous linear equations \[ x+y+z=6, \] \[ 5x-y+2z=3, \] \[ 2x+y-z=5, \] then \((Adj\,A)D=\)

If \(a,b,c\) are respectively the \(5^{th}, 8^{th}, 13^{th}\) terms of an arithmetic progression, then \[ \begin{vmatrix} a & 5 & 1\\ b & 8 & 1\\ c & 13 & 1 \end{vmatrix} = \]

Let \[ A= \begin{bmatrix} -2 & x & 1\\ x & 1 & 1\\ 2 & 3 & -1 \end{bmatrix} \] If the roots of the equation \[ \det(A)=0 \] are \(l,m\), then \[ l^3-m^3= \]