If B=\begin{bmatrix} 4 & 2\\ 1 & 3 \end{bmatrix} then find `B^2`

3. If \begin{equation*} A = \begin{bmatrix} 3 & 3 & 5 \\ 4 & 4 & 4 \\ \end{bmatrix} \end{equation*} and \begin{equation*} B = \begin{bmatrix} -3 & 4 \\ 2 & -5 \\ 1 & 1 \end{bmatrix} \end{equation*} Then find the value of AB

\begin{bmatrix} 1 & 6 \\ 7 & 2 \end{bmatrix} =P+Q , where P is Symmetric and Q is a skew-symmetric then P=

If A=\begin{bmatrix} 1 & 2 & 2\\ 2 & 1 & 2\\ 2 & 2 & 1 \end{bmatrix} , then show that A^2-4A-5I=O ,where I and 0 are the unit matrix and the null matrix of order 3, respectively. Use this result to find A^(-1)dot

\begin{bmatrix}6i&-3i&1\\ 4 &3i& -1\\ 20&3&i\\ \end{bmatrix} =x+i y , then a. x=3,y=1 b. x=1,y=3 c. x=0,y=3 d. x=0,y=0

If a ,\ b ,\ c are roots of the equation x^3+p x+q=0 , prove that detrminant of \begin{bmatrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{bmatrix} is zero

If A = {1, 2, 3} , B = {3, 4, 5} , then find A- B and B - A .

If the seventh term from the beginning and end in the binomial expansion of (2 3+1/(3 3))^n ,"" are equal, find ndot

If A=(1,2,3) and B=(3,4,5), then find A xx B .

If A=[(2,-1),(3,2)] and B =[(0,4),(-1,7)] , then find 3A^(2) -2B+1 .