List of top Mathematics Questions on Determinants asked in KCET

If A_n = $\begin{bmatrix} 1-n & n \\ n & 1-n \\ \end{bmatrix}$ then | A₁ | + | A₂ | + ….. + | A₂₀₂₁ | =

If there are two values of ‘a’ which makes determinant
$\Delta=\begin{bmatrix} 1 & -2 & 5 \\ 2 & a & -1 \\ 0 & 4 & 2a \\ \end{bmatrix}=86$
Then the sum of these numbers

If x³ - 2x² - 9x + 18 = 0 and A = $\begin{vmatrix}     1 & 2 & 3 \\     4 & x & 6 \\     7 & 8 & 9 \\ \end{vmatrix}$ then the maximum value of A is

If A and B are matrices of order 3 and |A| = 5, |B| = 3 then |3AB| is

If A is a square matrix of order 3 and |A| = 5, then |A adj.A| is

If the value of a third order determinant is $16$, then the value of the determinant formed by replacing each of its elements by its cofactor is

If $A$ is a square matrix of order $3 \times 3$, then $|KA|$ is equal to

If $x y z$ are not equal and $\neq$ 0, $\neq$ 1 the value of $\begin{vmatrix} \log x& \log y& \log z\\ \log 2x& \log 2y& \log 2z\\ \log 3x& \log 3y& \log 3z\end{vmatrix}$ is equal to

Evaluate $\left|\begin{array}{ll}\cos 15 & \sin 15 \\ \sin 75 & \cos 75\end{array}\right|$

If $\begin{vmatrix} {2a}&{x_1} &{y_1}\\ {2b}&{x_2}& {y_2} \\ {2c}&{x_3}&{y_3}\\ \end{vmatrix}$ $=$$\frac {abc}{2} \neq 0$, then the area of the triangle whose vertices are $(\frac {x_1}{a},\frac {y_1}{a})$$(\frac {x_2}{b},\frac {y_2}{b})$$(\frac {x_3}{c},\frac {y_3}{c})$ is

The inverse of the matrix $A =\begin{bmatrix} {2}&{0} &{0}\\ {0}&{3}& {0} \\ {0}&{0}&{4}\\ \end{bmatrix}$ is

If $A$ is a matrix of order $3$, such that $A (adj A) = 10\, I$, then $|adj A|$ =

If $a, b$ and $c$ are in A.P., then the value of $\begin{vmatrix} {x+2}&{x+3} &{x+a}\\ {x+4}&{x+5}& {x+b} \\ {x+6}&{x+7} &{x+c}\\ \end{vmatrix}$ is

If the determinant of the adjoint of a (real) matrix of order $3$ is $25$, then the determinant of the inverse of the matrix is

The characteristic equation of a matrix $A$ is $\lambda^3 - 5\lambda^2 - 3\lambda + 2 = 0$ then $| adj (A) |$ is equal to

If $A$ is a $3 \times 3$ nonsingular matrix and if $|A | = 3$, then $|(2A)^{-1}|$= _______

If $A=\begin{bmatrix} {2}&{1} &{0}\\ {0}&{2}& {1} \\ {1}&{0}&{2}\\ \end{bmatrix}$then$| adj A|$ =

If $\begin{vmatrix} {1+\sin^2}&{\cos^2 \theta } &{4\sin 2\theta}\\ {\sin^2}&{1+\cos^2}& {4\sin2\theta} \\ {\sin^2\theta}&{\cos^2\theta}&{4\sin2\theta-1}\\ \end{vmatrix} =0 $and$ 0< \theta

If $A =\begin{bmatrix} {1}&{-1} &{1}\\ {2}&{1}& {-3} \\ {1}&{1}&{1}\\ \end{bmatrix} ,10B \begin{bmatrix} {4}&{2} &{2}\\ {-5}&{0}& {\alpha} \\ {1}&{-2}&{3}\\ \end{bmatrix}$ and $B$ is the inverse of $A$, then the value of $\alpha$ is

If $A = \begin{bmatrix} {1}&{-2} &{2}\\ {0}&{2}& {-3} \\ {3}&{-2}&{4}\\ \end{bmatrix}$,then $A . adj(A)$ is equal to

The value of $\begin{vmatrix} x+y&y+z & z+ x \\[0.3em] x & y & z \\[0.3em] x-y & y-z & z-x \end{vmatrix}$ = is equal to :

If $A=\begin{bmatrix} {3}&{5}\\ {2}&{0}\\ \end{bmatrix}$ and $B$ = $\begin{bmatrix} {1}&{17}\\ {0}&{-10}\\ \end{bmatrix}$then $|AB|$ is equal to