Find the Inverse of the Resulting Matrix [[6,4]][[4,6]]

Problem

[[6,4]]*[[4],[6]]

Solution

1. Multiply the matrices to find the resulting value. Since we are multiplying a 1×2 matrix by a 2×1 matrix, the result is a 1×1 matrix (a scalar).

[[6,4]]*[[4],[6]]=(6⋅4)+(4⋅6)

24+24=48

2. Identify the resulting 1×1 matrix.

A=[48]

3. Apply the formula for the inverse of a 1×1 matrix. For a matrix A=[a] the inverse is A(−1)=[1/a] provided a≠0

A(−1)=[1/48]

Final Answer

([[6,4]]*[[4],[6]])(−1)=[(1/48)]

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