I have to show that a matrix of one, denoted $J_n$ is not invertible.
To begin with I proved by going back to the definition that $J_n^2 = nJ_n$ but now I have to deduce from this that $J_n$ is not invertible.
Does anyone have a clue ?
2026-04-29 14:23:09.1777472589
Inverse of a matrix of one.
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The matrix has row rank $1$ and so is singular if $n>1$.
Note that the 2x2 matrix $A=2I$ is invertible and yet $A^2=2A$ so it is not possible to argue from $J_n^2 = nJ_n$ only.