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Mar
12
comment If $A,B\in M_2(\mathbb{R})$, show that $(AB-BA)(AB-BA)$ is a scalar matrix.
@MichaelBiro No. The book I'm using still didn't introduce it. So I suppose it can't be used (I usually answer the books trying to using only what is given, I guess the authors expect that from the students) - But I'll look for it because I'm curious. Thanks!
Mar
12
asked If $A,B\in M_2(\mathbb{R})$, show that $(AB-BA)(AB-BA)$ is a scalar matrix.
Mar
11
awarded  Popular Question
Mar
10
asked If $A,B$ are invertible, show that $AB$ is invertible and express $(AB)^{-1}$ in terms of $A^{-1},B^{-1} $.
Mar
8
accepted When is an upper triangular matrix invertible?
Mar
8
comment When is an upper triangular matrix invertible?
Very good. That was one of the possible ways I was thinking about.
Mar
8
comment When is an upper triangular matrix invertible?
Please, see my reply to John Wayland.
Mar
8
comment When is an upper triangular matrix invertible?
Please, see my reply to John Wayland.
Mar
8
comment When is an upper triangular matrix invertible?
@JohnWaylandBales Yes, but I'm trying to do without the notion of determinant which wasn't introduced in the book yet. But perhaps, solving the exercise means exactly developing the determinant.
Mar
8
asked When is an upper triangular matrix invertible?
Mar
3
awarded  Nice Answer
Feb
26
awarded  Yearling
Feb
26
asked If $a>0$, then $b<0 \implies ab < 0 $?
Feb
13
awarded  Favorite Question
Feb
13
comment How do I prove that sine is dependent only on the angle?
@YvesDaoust Yes. Sine has two meanings, it is the single function argument and It is also the ratio of two sides of the right triangle (opposite/hypotenuse). As this ratio depends only on the angle, one can simplify things and get $h=1$ and hence: $opposite/1=opposite$. (I guess this is correct).
Feb
13
comment How do I prove that sine is dependent only on the angle?
@YvesDaoust I'm talking about this definition.
Feb
13
comment How do I prove that sine is dependent only on the angle?
@YvesDaoust Yes, I know. But I'm talking about that definition.
Feb
13
comment How do I prove that sine is dependent only on the angle?
@YvesDaoust Uh?
Feb
13
comment How do I prove that sine is dependent only on the angle?
@GiovanniResta Is there a remedy to this? For example, adding it to the hypotenuse?
Feb
13
asked How do I prove that sine is dependent only on the angle?