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.