‫Welcome back.
‫Today, we're going to talk about an interesting category of mattresses which are called also normal
‫mattresses or the normal mattresses are mattresses whose inverse equals their transpose.
‫So normally, if we have a matrix, a then it's inverse would be a superscript minus one.
‫And it has to follow this relationship a times.
‫A inverse equals a inverse times A equals ie, which is the identity matrix.
‫For example, a 3-D identity matrix looks like this.
‫You have three ones here in the diagonal and the rest of the elements are zeros.
‫It's like one when we work with scalars.
‫However, if A is also an author normal matrix, then a inverse equals a transposed.
‫Therefore you can say that a times a transposed equals a transposed times A equals the identity matrix.
‫Now the thing is that our three rotation matrices that we had derived in the previous videos are also
‫also normal matrices.
‫Because of that fact, it is very easy for you to find their inverses.
‫So to find the inverse of our sub X are sub Y and our Sabzi, which are the rotation matrices about
‫their respective axes, you just need to take their transpose.
‫So here's another exercise for you.
‫Find the inverse of these three rotation matrices and you will see the solution in the next video.
‫See you there.