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If $\text{A}=[\text{a}_\text{ij}]_{\text{m}\times\text{n}}$ and $\text{B}=[\text{b}_\text{ij}]_{\text{m}\times\text{n}}$ are two matrices, then A ± B is of order m × n and is defined as:
$(\text{A}\pm\text{B})_\text{ij}=\text{a}_\text{ij}\pm\text{b}_\text{ij},$ where i = 1, 2, ............. , m and j = 1, 2, .......... , n
If $\text{A}=[\text{a}_\text{ij}]_{\text{m}\times\text{n}}$ and $\text{B}=[\text{b}_\text{ij}]_{\text{n}\times\text{p}}$ are two matrices, then AB is of order m × p and is defined as:
$(\text{A}\text{B})_\text{ik}=\sum\limits_\text{r=1}^\text{n}\text{a}_\text{ir}\text{b}_\text{rk}=\text{a}_\text{i1}\text{b}_\text{1k}+\text{a}_\text{i2}\text{b}_\text{2k}+.....+\text{a}_\text{in}\text{b}_\text{nk}$
Consider $\text{A}=\begin{bmatrix}2&-1\\3&4\end{bmatrix},\ \text{B}=\begin{bmatrix}5&2\\7&4\end{bmatrix},\ \text{B}=\begin{bmatrix}2&5\\3&8\end{bmatrix} \text{And}\ \text{D}=\begin{bmatrix}\text{a}&\text{b}\\\text{c}&\text{d}\end{bmatrix}$
Using the concept of matrices answer the following questions.

1. Find the product AB.

1. $\begin{bmatrix}3&0\\43&22\end{bmatrix}$
2. $\begin{bmatrix}0&3\\22&43\end{bmatrix}$
3. $\begin{bmatrix}43&22\\0&3\end{bmatrix}$
4. $\begin{bmatrix}22&43\\3&0\end{bmatrix}$

2. If A and Bare any other two matrices such that AB exists, then

1. BA does not exist.
2. BA will be equal to AB.
3. BA may or may not exist.
4. None of these.

3. Find the values of a and c in the matrix D such than CD - AB = 0.

1. a = 77, c = -191
2. a = -191, c = 77
3. a = 191, c = 77
4. a = 91, c = 70

4. Find the values of band din the matrix D such that CD - AB = 0.

1. b = 44, d = -110
2. b = 110, d = 44
3. b = -110, d = 44
4. b = -44, d = 110

5. Find B + D.

1. $\begin{bmatrix}80&200\\115&105\end{bmatrix}$
2. $\begin{bmatrix}84&48\\180&181\end{bmatrix}$
3. $\begin{bmatrix}186&108\\-84&-48\end{bmatrix}$
4. $\begin{bmatrix}-186&-108\\84&48\end{bmatrix}$