Obviously a 2 =

0 1 0

0 0 1

1 0 0

And a 3 =

1 0 0

0 1 0

0 0 1 is identity matrix e.

therefore

A^ 100

=(A^3)^33 *A

=A

but

A^(- 1)

=A^(- 1) *E

=A^(- 1) *A^3

=A^2=

0 1 0

0 0 1

1 0 0

2、

2B^2=tB，

By calculating the determinants on both sides of the equation at the same time,

|2B*B|=|tB|，

Obviously, the determinant of b transposition is equal to the determinant of b, that is |tB|=|B|,

but

2B*B|

=|2B|*|B|

=2^n *|B|*|B|，

So 2 n * | b | *| b | = | b |,

That is | b | = 1/2 n,

The determinant of b is1/2 n n.