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Algebra 2SuperchallengeLinear Systems & Matrices

Linear Systems & Matrices · Superchallenge problem

The matrix

M=[1234412334122341]M = \begin{bmatrix} 1 & 2 & 3 & 4 \\ 4 & 1 & 2 & 3 \\ 3 & 4 & 1 & 2 \\ 2 & 3 & 4 & 1 \end{bmatrix}

is invertible. Find the sum of all sixteen entries of M−1M^{-1}.