Question

if A=[(1 -5) (6 4)] , B =[(1 0) (0 -1)] find the matrix AB-2I​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

Given That:

$\rm\implies A=\begin{bmatrix}1&-5\\ 6&4\end{bmatrix}$

$\rm\implies B=\begin{bmatrix}1&0\\ 0&-1\end{bmatrix}$

We have to find out the matrix AB - 2I. Which is -

$\rm\implies AB-2I=\begin{bmatrix}1&-5\\ 6&4\end{bmatrix}\begin{bmatrix}1&0\\ 0&-1\end{bmatrix}-2\begin{bmatrix}1&0\\ 0&1\end{bmatrix}$

$\rm\implies AB-2I= \begin{bmatrix}1 - 0&0 + 5\\ 6 + 0&0 - 4\end{bmatrix}-\begin{bmatrix}2&0\\ 0&2\end{bmatrix}$

$\rm\implies AB-2I= \begin{bmatrix}1 &5\\ 6& - 4\end{bmatrix}-\begin{bmatrix}2&0\\ 0&2\end{bmatrix}$

$\rm\implies AB-2I= \begin{bmatrix}1 - 2&5 - 0\\ 6 - 0& - 4 - 2\end{bmatrix}$

$\rm\implies AB-2I= \begin{bmatrix} - 1&5\\ 6& - 6\end{bmatrix}$

Which is our required answer.

$\textsf{\large{\underline{Learn More}:}}$

Matrix: A matrix is a rectangular arrangement of numbers in the form of horizontal and vertical lines.

Horizontal lines are called rows and vertical lines are called columns.

Order of Matrix: A matrix containing x rows and y column has order x × y and it has xy elements.

Different types of matrices:

Row Matrix: This type of matrices have only 1 row. Example:

$\rm\implies A=\begin{bmatrix}\rm 1&\rm 2&\rm 3\end{bmatrix}$

Column Matrix: This type of matrices have only 1 column. Example:

$\rm\implies A=\begin{bmatrix}\rm1\\ \rm2\\ \rm3\end{bmatrix}$

Square Matrix: In this type of matrix, number of rows and columns are equal. Example:

$\rm\implies A=\begin{bmatrix}\rm 1&\rm 2\\ \rm 3&\rm 4\end{bmatrix}$

Zero Matrix: It is a matrix with all elements present is zero. Example:

$\rm\implies A=\begin{bmatrix}\rm 0&\rm 0\\ \rm 0&\rm 0\end{bmatrix}$

Identity Matrix: In this type of matrix, diagonal element is 1 and remaining elements are zero. An Identity matrix is always a square matrix. Example:

$\rm\implies A=\begin{bmatrix}\rm 1&\rm 0\\ \rm 0&\rm 1\end{bmatrix}$