Question

A and B are two 2x2 matrices that A =1 2 and B= 5 -2. Find AB. 2 5 -2 1

Answer 1

Answer:

Therefore,

$AB=\left[\begin{array}{cc}1&0\\0&1\\\end{array}\right]$

Step-by-step explanation:

Given:

Matrix A and B

$A =\left[\begin{array}{cc}1&2\\2&5\\\end{array}\right] \\\\\\B =\left[\begin{array}{cc}5&-2\\-2&1\\\end{array}\right]$

To Find:

AB = ?

Solution:

First step to check multiplication is exist or not

If number of columns of A matrix is equal to number of rows of  B matrix

then Multiplication of AB exist

Here it is equal  that is 2

So,

$AB=\left[\begin{array}{cc}1&2\\2&5\\\end{array}\right]\left[\begin{array}{cc}5&-2\\-2&1\\\end{array}\right] \\\\\\AB=\left[\begin{array}{cc}1\times 5+2\times -2&1\times -2+2\times 1\\2\times 5+5\times -2&2\times -2+5\times 1\\\end{array}\right]\\\\\\AB=\left[\begin{array}{cc}1&0\\0&1\\\end{array}\right]$

Which is an Identity Matrix

Therefore,

$AB=\left[\begin{array}{cc}1&0\\0&1\\\end{array}\right]$