List of top Mathematics Questions on Properties of Determinants asked in MHT CET

If \(A = \begin{bmatrix} 1 & -2 & 2 0 & 2 & -3 3 & -2 & 4 \end{bmatrix}\), find the value of the matrix expression \(A(I + \text{adj } A)\), where \(I\) is the identity matrix of the same order as \(A\).

If \(A\) is a \(3\times3\) matrix such that \(|A| = 4\) and \(B = \text{adj}\,A\), find the value of \(|B|\).

The vectors $\vec{p} = \hat{i} + a\hat{j} + a^2\hat{k}, \vec{q} = \hat{i} + b\hat{j} + b^2\hat{k}$ and $\vec{r} = \hat{i} + c\hat{j} + c^2\hat{k}$ are non-coplanar and $\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0$ then the value of $(abc)$ is

The vectors $\vec{p} = \hat{i} + a\hat{j} + a^2\hat{k}, \vec{q} = \hat{i} + b\hat{j} + b^2\hat{k}$ and $\vec{r} = \hat{i} + c\hat{j} + c^2\hat{k}$ are non-coplanar and $\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0$ then the value of $(abc)$ is

The vectors $\vec{p} = \hat{i} + a\hat{j} + a^2\hat{k}, \vec{q} = \hat{i} + b\hat{j} + b^2\hat{k}$ and $\vec{r} = \hat{i} + c\hat{j} + c^2\hat{k}$ are non-coplanar and $\begin{vmatrix} a & a^2 & 1+a^3 \\ b & b^2 & 1+b^3 \\ c & c^2 & 1+c^3 \end{vmatrix} = 0$ then the value of $(abc)$ is

Let \( A=\begin{bmatrix}2 & -1 \\ 0 & 2\end{bmatrix} \). If \( B=I-{}^{3}C_{1}(\mathrm{adj}\,A)+{}^{3}C_{2}(\mathrm{adj}\,A)^{2}-{}^{3}C_{3}(\mathrm{adj}\,A)^{3} \), then the sum of all elements of the matrix \( B \) is