Amit M Agarwal Solutions for Chapter: Matrix, Exercise 3: Target Exercises

If $A$ is a skew-symmetric matrix, then trace of $A$ is

Let $A$ and $B$ be two symmetric matrices of same order. Then, the matrix $AB-BA$ is

If $A=\left[\begin{array}{lll}6& 8& 5\\ 4& 2& 3\\ 9& 7& 1\end{array}\right]$ is the sum of a symmetric matrix $B$ and skew-symmetric matrix $C$, then $B$ is

If $A=\left[\begin{array}{rr}-1& \frac{3}{2}\\ -\frac{1}{2}& \frac{1}{2}\end{array}\right]$, then $I+A+A^2+\dots$ is equal to

If $A$ is a square matrix, then 

Let $A=\left[\begin{array}{ccc}1& -1& 1\\ 2& 1& -3\\ 1& 1& 1\end{array}\right]$ and $10B=\left[\begin{array}{ccc}4& 2& 2\\ -5& 0& \alpha \\ 1& -2& 3\end{array}\right]$. If $B$ is the inverse of matrix $A$, then $\alpha$ is equal to

If $A$ and $B$ are square matrices of size $n\times n$ such that $A^2-B^2=\left(A-B\right)\left(A+B\right)$, then which of the following will always be true?

If $A=\left[\begin{array}{ll}1& 2\\ 5& 4\end{array}\right]$, then a non-singular matrix $P$ such that $P^{-1}AP=\left[\begin{array}{cc}6& 0\\ 0& -1\end{array}\right]$, is