If A = $\left(\begin{array}{l l}{{0}}&{{3}}\\ {{2}}&{{-5}}\end{array}\right)$ and $K A\ =\ {\left(\begin{array}{l l}{0}&{4a}\\ {-8}&{5b}\end{array}\right)}$ find the values of k and a.

Find matrix A such that. $\left(\begin{array}{l l}{2}&{-1}\\ {1}&{0}\\ {-3}&{4}\end{array}\right)$ $A={\left(\begin{array}{l l}{-1}&{-8}\\ {1}&{-2}\\ {9}&{22}\end{array}\right)}$

Let A = $A\ =\ {\left(\begin{array}{l l}{2}&{-1}\\ {3}&{4}\end{array}\right)}$ , B = $A\ =\ {\left(\begin{array}{l l}{5}&{2}\\ {7}&{4}\end{array}\right)}$ , C = $A\ =\ {\left(\begin{array}{l l}{2}&{5}\\ {3}&{8}\end{array}\right)}$ , find a matrix D such that CD - AB = 0.

Give an example of a skew symmetric matrix of order 3.

Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3.

Write the element $a_{23}$ of a 3 × 3 matrix A = ($a_{i j}$) whose elements $a_{i j}$ are given by $a_{i j}=\frac{|i-j|}{2}$

If A is a square matrix such that A² = I, then find the simplified value of (A – I)³ + (A + I)³ – 7A.

If ${\left[\begin{array}{l l}{x y}&{4}\\ {z+6}&{x+y}\end{array}\right]}\ ={\left[\begin{array}{l l}{8}&{w}\\ {0}&{6}\end{array}\right]},$ write the value of x + y + z.

The elements $a_{i j}$ of a 3 × 3 matrix are given by $a_{i j}=\,\frac{1}{2}\,\vert-3i+j\vert.$. Write the value of element $a_{32}$.

If $(2x\ \ 4){\binom{x}{-8}}=0,$ find the positive value of x.

If A is a square matrix such that A² = A, then write the value of 7A – (I + A)³, where I is an identity matrix.

If ${\left[\begin{array}{l l}{a+4}&{3b}\\ {8}&{-6}\end{array}\right]}={\left[\begin{array}{l l}{2a+2}&{b+2}\\ {8}&{a-8b}\end{array}\right]},$ write the value of a – 2b.

If 2 $\left(\begin{array}{l l }3 & 4 \\ 5 & x\end{array}\right)$ + $\left(\begin{array}{l l }1 & y \\ 0 & 5\end{array}\right)$ = $\left(\begin{array}{l l }7 & 0 \\ 10 & 5\end{array}\right)$ find x - y.

Solve the following matrix equation for x : [x 1] $\left(\begin{array}{l l }1 & 0 \\ -2 & 0\end{array}\right)$ = 0.

If $\left(\begin{array}{l l }x-y & z \\ 2x-y & w\end{array}\right)$ = $\left(\begin{array}{l l }-1 & 4 \\ 0 & 5\end{array}\right)$ , find the value of x + y.