We need to put a suitable entry in that spot so as to obtain

A A^-1 = I    The Identity Matrix

For the moment, let us put an "x" in that spot. Then, multiplying the first row of A by the first column of A^-1 gives:

(1)(x) + (0)(-28) + (-2)(3) = x - 6.

However, we are surpposed to get the (1,1) entry of the indentity matrix; namely 1. Thus,

x - 6 = 1

Which says that x must be 7.

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