Matrices are your friends.

Algebra Level 5

C=[1437]\large C = \begin{bmatrix} -1 & 4 \\ -3 & 7 \end{bmatrix}

It is given that the multiplicative inverse of 6C5I 6C - 5I can be expressed as below, where kk, mm, and nn are positive integers, and II is the identity matrix.

1k(CnI)m \large \frac{1}{k} {(C - nI)}^{m}

What is k+m+n+3k + m + n + 3?

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