Embibe Experts Solutions for Chapter: Matrices and Determinants, Exercise 1: KEAM 2019

If $AB=A$ and $BA=B,$ then $A^2,B^2$ is equal to

If $\left|\begin{array}{lll}1& a& a^2\\ 1& x& x^2\\ b^2& ab& a^2\end{array}\right|=0$, then $x=$

A determinant of second order is made up of elements $0$ and $1.$ The number of determinants with non-negative values is

The points $(k, 2-2 k),(-k+1,2 k)$ and $(-4-k, 6-2k)$ are collinear for

If $\alpha , \beta$ and $\gamma$ are the roots of the equation $x^3+px+q=0,$ then the value of the determinant $\left|\begin{array}{lll}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta \end{array}\right|$ is

If $A$ is an invertible matrix of order $n$ and $k$ is any positive real number, then the value of $[det\left(kA\right){]}^{-1}det(A)$ is

If $A$ be a square matrix of order $n$ and if $\left|A\right|=D$ and $\left|adj A\right|=D\text{'}$, then

The system of equations

$\mathrm{x}+\mathrm{y}+2\mathrm{z}=4$

$3\mathrm{x}+3\mathrm{y}+6\mathrm{z}=17$

$5\mathrm{x}-3\mathrm{y}+2\mathrm{z}=27$ has