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.)

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.)
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Solution

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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.

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