Algebra of Matrices Maths - Algebra of Matrices

1. B
2. n^B
3. Bⁿ
4. A + B

1. Only AB is defined.
2. Only BA is defined.
3. AB and BA both are defined.
4. AB and BA both are not defined.

1. 3
2. 4
3. 6
4. 7

1. I
2. A
3. O
4. -I

$\text{A}=\begin{bmatrix}\text{a}+4&3\text{b}\\8&-6\end{bmatrix},\text{ B}=\begin{bmatrix}2\text{a}+2&\text{b}^2+2\\8&\text{b}^2-5\text{b}\end{bmatrix}$

The number of contacts of each type made in two cities X and Y is given in matrix B as

$\text{BA}=\begin{bmatrix}\text{Telephone}&\text{House call}&\text{Letter}\\1000&500&5000\\3000&1000&10000\end{bmatrix} \begin{matrix}\rightarrow\text{X}\\\rightarrow\text{Y}\end{matrix}$

Find the total amount spent by the group in the two cities X and Y.