# Tagged Questions

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### Find the inverse with respect to the binary operation $a ∗ b = a + b + a^2 b^2$

A binary operation on $\mathbb{R}$: $a * b = a + b + a^2 b^2$ The neutral element I found to be $0$. Then I need to find an invertible element having two distinct inverses. I don't know where to ...
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I'd like a hint rather than a full solution. The problem I am considering is the following: $X$ is an $n\times m$ matrix $Y$ is $m\times n$ Show that $(I - XY)^{-1}\cdot X = X\cdot(I - ... 2answers 40 views ### for$k\neq 0, -1, 1$, find the inverse of the matrix for$k\neq 0, -1, 1$, find the inverse of the matrix $$\begin{pmatrix} k&0&0\\ 1&k&1\\ -1&1&k \end{pmatrix}$$ how am I supposed to solve this? all I can think of is plugging ... 0answers 14 views ### Study the associative and commutative properties and neutral and inverse elements of these groups Group m*n = max(m,n) on Z and N So i showed its associative by m,n,p in Z and (m*n)*p = max(m,n)p =max(m,n,p) And m(n*p) = m*max(n,p) = max(m,n,p) Commutative m*n = max(m,n) and n*m = max(n,m). I ... 1answer 42 views ### expansion of matrix inverse I would like to invert a square matrix$L$. One can write it as a sum of two matrices, one containing the diagonal terms ($D$) and the other the off-diagonal ones ($A$). $$L = D+A$$ I would like ... 2answers 62 views ### Showing that a matrix is invertible and finding its inverse I'm incredibly rusty at linear algebra, and in preparation for my course I've been doing some review questions. I've been staring at this one for a half hour and still don't know how to approach it: ... 1answer 21 views ### Case Deletion Diagnostics I have NO idea how to approach this problem. I don't see any connection between the corollary and the formula we need to prove. Does anyone have any hints? Corrolary: If$\mathbf{A}$and ... 0answers 16 views ### Calculating the left pseudoinverse of a Matrix whose columns are Probablity Mass Functions I have a matrix$A_{m\times n}$, where$A_j$, a column of$A$represents a probability mass function, and so the sum over the column is 1. This is true for all the columns of A, i.e.$\forall j \in ...
Let A be a $2 \times 2$ matrix whose inverse also exists. If I was to draw a line from each of the 3 vertices (that are not the origin) of the determinant of A, to the 3 vertices of the determinant of ...