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What are some uses of an inverse matrix? (besides decoding messages)

Given a matrix |A| multiplied by its inverse |A|^-1 results in the Unit matrix |1| where the unit matrix has diagonal elements equal to unity, that is equal to 1, and all other non-diagonal matrix elements equal to 0. So for a square matrix of coefficients |A| the inverse matrix |A|^-1 is the solution of the "n" equations in "n" unknowns. This is but one of many applications of finding the inverse of a matrix.

Vince Calder


One significant use of an inverse matrix is in mathematical problem-solving. Often a set of quantities related to one another can be transformed from initial to final values by means of matrix multiplication. The matrix multiplied by the set of initial values yields the set of final values. Quite often the reverse is needed. You know how things ended up and need to know how things must have been initially. Multiply the set of final values counters the effect of the matrix, yielding the set of initial values.

Dr. Ken Mellendorf

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