R K Bansal Solutions for Exercise 1: EXERCISE

If $\mathrm{A}$ and $\mathrm{B}$ are two matrices of orders $3\times 2$ and $2\times 3$ respectively; then their sum$\mathrm{A}+\mathrm{B}$is possible.

The matrices ${\mathrm{A}}_{2\times 3}$ and ${\mathrm{B}}_{2\times 3}$ are conformable for subtraction.

Transpose of a$2\times 1$ matrix is a$2\times 1$ matrix.

Transpose of a square matrix is a square matrix.

A column matrix has many columns and only one row.

If $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ are matrices of order $2\times 2,$ $(\mathrm{A}-\mathrm{B})·\mathrm{C}=\mathrm{A}·\mathrm{C}-\mathrm{B}·\mathrm{C}$.

If $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ are matrices of order $2\times 2,$ than ${\mathrm{A}}^2-{\mathrm{B}}^2=(\mathrm{A}+\mathrm{B})(\mathrm{A}-\mathrm{B})$.

If $\mathrm{A},\mathrm{B}$ and $\mathrm{C}$ are matrices of order $2\times 2,$ than $(\mathrm{A}-\mathrm{B}{)}^2={\mathrm{A}}^2-2\mathrm{A}·\mathrm{B}+{\mathrm{B}}^2$.