Embibe Experts Solutions for Chapter: Matrices and Determinants, Exercise 1: KCET (UG) 2020

If $A=\left[\begin{array}{ccc}1& -2& 1\\ 2& 1& 3\end{array}\right], B=\left[\begin{array}{ll}2& 1\\ 3& 2\\ 1& 1\end{array}\right]$ then ${\left(AB\right)}^T$ is equal to

If $f\left(x\right)=\left|\begin{array}{ccc}\cos x& 1& 0\\ 0& 2\cos x& 3\\ 0& 1& 2\cos x\end{array}\right|,$ then $\underset{x\to \pi }{\lim }f\left(x\right)=$

If $x^3-2x^2-9x+18=0$ and $A=\left|\begin{array}{lll}1& 2& 3\\ 4& x& 6\\ 7& 8& 9\end{array}\right|$ then the maximum value of $A$ is

The value of the determinant $\left|\begin{array}{ccc}a-b& b+c& a\\ b-c& c+a& b\\ c-a& a+b& c\end{array}\right|$

Let $A$ be a square matrix of order $3\times 3$, then $\left|5A\right|=$

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

Let $M$ be $2\times 2$ symmetric matrix with integer entries, then $M$ is invertible if

If $A$ and $B$ are invertible matrices then which of the following is not correct?