Questions: Determine whether the given matrices are inverses of each other by computing their product.
A= [5 1; 2 -1], B= [-1 1; 2 -4]
(Type an integer or simplified fraction for each matrix element.)
Transcript text: Determine whether the given matrices are inverses of each other by computing their product.
\[
A=\left[\begin{array}{rr}
5 & 1 \\
2 & -1
\end{array}\right], B=\left[\begin{array}{rr}
-1 & 1 \\
2 & -4
\end{array}\right]
\]
(Type an integer or simplified fraction for each matrix element.)
Solution
Solution Steps
Step 1: Compute the Product \(AB\)
The product \(AB\) is calculated as follows:
\[AB = [[-3, 1],
[-4, 6]]\]
Step 2: Compute the Product \(BA\)
The product \(BA\) is calculated as follows:
\[BA = [[-3, -2],
[ 2, 6]]\]
Step 3: Check for Identity Matrix
The identity matrix \(I\) of the same dimension is:
\[I = [[1., 0.],
[0., 1.]]\]
Checking if \(AB = I\) and \(BA = I\):
\[AB = I: False\]
\[BA = I: False\]
Final Answer:
Matrices \(A\) and \(B\) are not inverses of each other.