List of top Mathematics Questions on Determinants asked in AIEEE

Let A and B be real matrices of the form $\begin{bmatrix}\alpha&0\\ 0&\beta\end{bmatrix}$ and $\begin{bmatrix}0&\gamma\\ \delta&0\end{bmatrix}$, respectively. AB - BA is always an invertible matrix. AB-BA is never an identity matrix.

The number of values of k for which the linear equations $4x + ky + 2z = 0$ , $kx + 4y + z = 0$ and $2x + 2y + z = 0$ possess a non-zero solution is

Let A be a $2 \times 2$ matrix with non-zero entries and let $A^2 = I$, where I is $2 \times 2$ identity matrix. Define Tr(A) = sum of diagonal elements of A and $|A|$ = determinant of matrix A. $Tr(A) = 0$ $|A| = 1$

Consider the system of linear equations; $x_1 + 2x_2 + x_3 = 3$ $2x_1 + 3x_2 + x_3 = 3$ $3x_1 + 5x_2 + 2x_3 = 1 $ The system has

Let $A$ be a $2 \times 2$ matrix Statement-1 : adj (adj A) $= A$ Statement-2 : $|adj \,A| = |A|$

Let $A=\begin{vmatrix} 5& 5\alpha & \alpha \\[0.3em] 0 &\alpha &5\alpha \\[0.3em] 0 &0& 5 \end{vmatrix}$ , If $\left|\,A^2\,\right|=25$,then $\left|\,\alpha\,\right|$ equals

The system of equations $\alpha \, x + y + z = \alpha - 1$ $x + \alpha y + z = \alpha - 1$ $x + y + \alpha z = \alpha - 1$ has infinite solutions, if $\alpha$ is

If $a_1, a_2, a_3,......, a_n $,.... are in G.P., then the value of the determinant $\begin{vmatrix}\log a_{n}& \log a_{n+1}&\log a_{n+2}\\ \log a_{n+3}& \log a_{n+4}&\log a_{n+5}\\ \log a_{n+6} &\log a_{n+7}& \log a_{n+8}\end{vmatrix} $, is

If $1,\omega,\omega^2$ are the cube roots of unity, then $\Delta=\begin{vmatrix} 1&\omega^n &\omega^{2n} \\[0.3em] \omega^n &\omega^{2n} & 1 \\[0.3em] \omega^{2n} &1& \omega^n \end{vmatrix}$ is equal to

If $a > 0$ and discriminant of $ax^2 + 2bx +c $ is -ve then $\begin{vmatrix}a&b&ax+b\\ b &c&bx+c\\ ax+b &bx+c&0\end{vmatrix} $ is equal to

If $(\omega\,\neq\,1)$ is a cube root of unity , then $ \begin{vmatrix} 1 &1+i+\omega^2 &\omega^2 \\[0.3em] 1-i&-1 & \omega^2-1 \\[0.3em] -i & -1+\omega-i& -1 \end{vmatrix}=$