Identity matrix

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An identity matrix of size nn is the n×nn\times n square matrix with elements equal to 11 on the main, or leading diagonal (the diagonal of elements ai,ja_{i,j} where i=ji = j, so a1,1,a2,2,an,na_{1,1},a_{2,2},\dots a_{n,n}) and 00 elsewhere. For example, XX is a 4×44\times4 identity matrix:

X=(1000010000100001)X = \begin{pmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{pmatrix}

Look at the following matrix AA:

A=(510203471087)A = \begin{pmatrix} -5 & 10 & 20 \\ 3 & 4 & -7 \\ 10 & -8 & 7 \end{pmatrix}Find the matrix BB such that A+BA + B is an identity matrix of size 3×33\times3. Write the matrix BB to the answer field.

For example, your output may look like this

-2 3 1
1 -1 -1
3 -3 1
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