Algebra of Matrices

If $A$ is a matrix of order $2 \times 3,$ $B$is a matrix of order $3\times 2 ,$then what in the order of matrix $\left(AB\right)\text{'}$

Show that for two matrices A and $B$, $\mathrm{tr}\left(\mathrm{AB}\right)\ne \mathrm{tr}\left(\mathrm{A}\right)\mathrm{tr}\left(\mathrm{B}\right)$

Trace of an identity matrix with order $n\times n$ is

Find the value of $\text{'}k\text{'}$. If $\left[\begin{array}{rr}3& -1\\ 1& 4\end{array}\right]+\left[\begin{array}{rr}-2& 4\\ 1& 3\end{array}\right]=\left[\begin{array}{cc}1& 3\\ 2& k\end{array}\right]$.

Find: $\left[\begin{array}{rr}3& 4\\ 1& 4\end{array}\right]+\left[\begin{array}{rr}-2& -1\\ 1& 3\end{array}\right]$

Find $x$ and $y$. If, $\left[\begin{array}{cc}x& 3x-y\\ 4& 7\end{array}\right]=\left[\begin{array}{ll}3& 2\\ 4& 7\end{array}\right]$.

Check weather given matrices of the order $3\times 3$ and $2\times 2$ are to be comparable or not?

If $P=\left[\begin{array}{ccc}2& -3& 8\\ 21& 6& -6\\ 4& -33& 19\end{array}\right], Q\left[\begin{array}{ccc}1& -29& -8\\ 2& 0& 3\\ 17& 15& 4\end{array}\right]$. Then the value of $\left(P+Q\right)\text{'}$ and $P\text{'}+Q\text{'}$ will be same.

$A=\left[\begin{array}{cc}9& 8\\ 2& -3\end{array}\right], B=\left[\begin{array}{cc}4& 2\\ 1& 0\end{array}\right]$. Find the value of $\left(AB\right)\text{'}$ and $B\text{'}A\text{'}$

If matrix $A=\left[\begin{array}{ccc}1& 2& 3\\ 4& 5& 6\end{array}\right]$. Find the transpose of matrix $A.$

Is the value of $AB$ and $BA$  same, if

$A=\left[\begin{array}{cc}-5& 7\\ 3& 6\end{array}\right], B=\left[\begin{array}{ccc}1& -2& 0\\ 3& 1& 5\end{array}\right]$

Which one is the condition for Multiplication of Two Matrices?

If $A=\left[\begin{array}{cc}1& 5\\ 2& 3\end{array}\right], B=\left[\begin{array}{cc}-1& 1\\ 5& -3\end{array}\right]$  and $C=\left[\begin{array}{cc}3& 1\\ 2& 1\end{array}\right]$then $\left(AB\right)C=A\left(BC\right)$, why? 

Using the matrix multiplication formula, find the product of the matrices $A\left(BA\right),$ where

$A=\left[\begin{array}{cc}1& 2\\ 2& 1\end{array}\right], B=\left[\begin{array}{cc}2& 1\\ 1& 2\end{array}\right]$

Subtraction of matrices is possible only if the order of matrices is the same.'

If $A=\left[\begin{array}{cc}3& 1\\ 2& 0\end{array}\right]$ and $C=3$, then $AC=$

Find the transpose for the given $2\times 2$ matrix, $X=\left[\begin{array}{cc}7& 11\\ 21& 16\end{array}\right]$

Give an example to show that the product of two non-zero matrices is a zero matrix.

Explain the Distributive Property of Matrix Multiplication over Addition

Explain the Multiplicative Identity in Matrices