Question

Find the inverse of the following matrix A, A^-1, if possible. Check that AA^-1=I and A^-1 A=I.

Answer 1

The Determinant of this matrix must be different from 0 so that its inverse can be found

So we calculate The determinant

this is the matrix on a general form

We apply a equation to find Determinant

The equation

And we replace for our case

then

`(-4\cdot-4\cdot4)+(0\cdot0\cdot0)+(-4\cdot-4\cdot-4)-(0\cdot-4\cdot-4)-(-4\cdot0\cdot-4)-(-4\cdot-4\cdot0)`

and solve, first parethesis

`\begin{gathered} 64+0-64-0-0-0 \\ =0 \end{gathered}`

this determinant is zero so the matrix has no inverse matrix

The inverse of the matrix A is no possible