Questions: Examine the product of the two matrices to determine if each is the inverse of the other. [ [3, -4], [4, -5] ] [ [-5, 4], [-4, 3] ] Are the matrices inverses of each other? No Yes

Examine the product of the two matrices to determine if each is the inverse of the other.

[ [3, -4], [4, -5] ] [ [-5, 4], [-4, 3] ]

Are the matrices inverses of each other?
No
Yes

Transcript text: Examine the product of the two matrices to determine if each is the inverse of the other. \[ \left[\begin{array}{ll} 3 & -4 \\ 4 & -5 \end{array}\right]\left[\begin{array}{ll} -5 & 4 \\ -4 & 3 \end{array}\right] \] Are the matrices inverses of each other? No Yes

Solution

Solution Steps

Step 1: Calculate the Product \(AB\)

Matrix \(A\) multiplied by matrix \(B\) gives matrix \(C\), calculated as [[1 0] [0 1]].

Step 2: Calculate the Product \(BA\)

Matrix \(B\) multiplied by matrix \(A\) gives matrix \(D\), calculated as [[1 0] [0 1]].

Step 3: Check for Identity Matrix

Both products \(AB\) and \(BA\) result in an identity matrix, indicating that \(B\) is indeed the inverse of \(A\).

Final Answer:

Matrix \(B\) is the inverse of matrix \(A\).

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