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# Further Math Matrices - Help!

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1. There's a question I really do not understand in one of the past papers:

It says M = -2 -1
3 1
And that M^3 is equal to the identity matrix.

The mark schemes says:

I should get the matrix
1 1
-3 -2

And multiply it by the original matrix.

I don't understand why I multiply them together, and how I get the matrix 11, -3 -2 in the first place
Attached Images

2. M^3

Means M x M x M

Do M x M first (you'll get the 1 1 -3 -2 matrix in the markscheme)

then multiply that answer by M again and you'll get the identity matrix.

If you can't multiply matrices, don't try and learn it now - just revise what you do know.

(Original post by FredTheBaker)
There's a question I really do not understand in one of the past papers:

It says M = -2 -1
3 1
And that M^3 is equal to the identity matrix.

The mark schemes says:

I should get the matrix
1 1
-3 -2

And multiply it by the original matrix.

I don't understand why I multiply them together, and how I get the matrix 11, -3 -2 in the first place
3. Okay, so you're wanting to find the matrix A^3. If you're cubing a number, you times it by itself 3 times. So to get A cubed, we times the matrix by itself once, and then take that and times that by the matrix. Think of it like this: the cube of 2 is 8. To get 8, we do 2 x 2 = 4 and then we do 4 x 2 = 8. Its the same for this matrix. We do A x A = A^2. Then we do A^2 x A = A^3. I don't know how you set out matrices, but I've done it for you. I took the matrix I got in image 1 (which is A^2) and in image 2 I multiplied it by A to get A^3, which is equal to the identity matrix.

.

Hopefully I've helped.
4. Kinda feel stupid now

Thanks

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