If the system of equations x = cy + bz, y = az + cx and z = bx + ay has a non - trivial solution then _____________

(a)

a² + b² + c² = 1

(b)

abc ≠ 1

(c)

a + b + c =0

(d)

a² + b² + c² + 2abc =1

If A^T is the transpose of a square matrix A, then ___________

(a)

|A| ≠ |A^T|

(b)

|A| = |A^T|

(c)

|A| + |A^T| =0

(d)

|A| = |A^T| only

If A is a square matrix that IAI = 2, than for any positive integer n, |Aⁿ| = _______

(a)

0

(b)

2n

(c)

2ⁿ

(d)

n²

If A is a square matrix of order n, then |adj A| = ______________

(a)

|A|^n-1

(b)

|A|^n-2

(c)

|A|ⁿ

(d)

None

If A =\(\left( \begin{matrix} cosx & sinx \\ -sinx & cosx \end{matrix} \right) \) and A(adj A) =\(\lambda \) \(\left( \begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix} \right) \) then \(\lambda \) is ________

(a)

sinx cosx

(b)

1

(c)

2

(d)

none