General statement for M^n in terms of aX and bY

[flutterfly]

Matrix binomials...please help!

Find the general statement that express Mⁿ in terms of aX and bY if:
A = aX and B = bY
$$M = \begin{pmatrix} a+b & a-b \\a-b & a+b \end{pmatrix}$$
M = A + B
M² = A² + B²
$$X = \begin{pmatrix} 1 & 1 \\1 & 1 \end{pmatrix}$$
$$Y = \begin{pmatrix} 1 & -1 \\-1 & 1 \end{pmatrix}$$

How would i do this question:... is it a matter of LS and RS check?
Test the validity of your general statement by using different values of a, b, and n?

 

[lanedance]

i don't understand your question - note the following tex to help write a matrix
$$A = \begin{pmatrix} a & b \\c & d \end{pmatrix}$$

 

[Dick]

What are XY and YX? If you expand (A+B)^n what terms can you eliminate? How can you simplify the remaining terms?