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Matrices Problems!!!!!

1. The point P(x,y,z) is mapped on the point Q (X,Y,Z) by the relation
(XYZ)\begin{pmatrix} X \\ Y \\ Z \end{pmatrix} = M (xyz)\begin{pmatrix} x \\ y \\ z \end{pmatrix} where M =

(120202021)\begin{pmatrix} -1 & 2 & 0 \\2 & 0 & -2 \\0 & -2 & 1 \end{pmatrix}


Show that M^3 = λ M and give the value or λ



2. A = (420202021)\begin{pmatrix} 4 & -2 & 0 \\-2 & 0 & -2 \\0 & -2 & 1 \end{pmatrix}
Given that the matrix P is such that P1APP^-1AP is a diagonal matrix B, write down a possible form for B

Also, can someone give me instruction on how to write maths equation in this forum?

Thanks in advance
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