### Video Transcript

Consider the matrix ๐ด equals
negative three, one, negative two, five. Find ๐ด inverse inverse.

Recall the definition of the
inverse of ๐ด is the matrix such that ๐ด multiplied by ๐ด inverse equals the
identity matrix. We do have a method for finding the
inverse of a two-by-two matrix. That is, given the matrix ๐ equals
๐, ๐, ๐, ๐, ๐ inverse is equal to one over ๐๐ minus ๐๐ multiplied by the
matrix ๐, negative ๐, negative ๐, ๐. So to find the inverse of the
inverse of ๐ด, we could use this method to find the inverse of ๐ด and then repeat
the method to find the inverse of that.

However, we do have one property of
the matrix inverse that can help us to do this a little bit quicker. That is, the inverse of the inverse
of ๐ด is just equal to ๐ด. So if we take a matrix and find its
inverse and then invert that matrix, we get the original matrix back. So, actually, the inverse of the
inverse of our matrix ๐ด is just the matrix ๐ด negative three, one, negative two,
five.