Embibe Experts Solutions for Exercise 1: EXERCISE

Which of the following is not true?

If $k$ is a scalar and $I$ is a unit matrix of order $3$, then $adj\left(kI\right)=$

Which of the following is/are true?

(i) Adjoint of a symmetric matrix is symmetric 

(ii) Adjoint of a unit matrix is a unit matrix  

(iii) $A\left(adjA\right)=\left(adjA\right)A=\left|A\right|I$ and 

(iv) Adjoint of a diagonal matrix is a diagonal matrix .

The adjoint of $\left[\begin{array}{ccc}1& 1& 1\\ 1& 2& -3\\ 2& -1& 3\end{array}\right]$ is -

The inverse of $\left[\begin{array}{ccc}1& 2& 3\\ 0& 1& 2\\ 0& 0& 1\end{array}\right]$ is -

If $A$ and $B$ are non-singular square matrices of same order, then $adj\left(AB\right)$ is equal to -

If $I_3$ is the identity matrix of order $3,$ then $I_3^{-1}$ is -

$A=\left[\begin{array}{lll}1& 0& 0\\ 0& 1& 1\\ 0& -2& 4\end{array}\right], I=\left[\begin{array}{lll}1& 0& 0\\ 0& 1& 0\\ 0& 0& 1\end{array}\right]$,  $A^{-1}=\frac{1}{6}\left(A^2+cA+dI\right)$ where $c,d\in R,$ then pair of values $(c,d)$ is