If |adj(adj A)| = |A|⁹, then the order of the square matrix A is

(a)

3

(b)

4

(c)

2

(d)

5

If A = \(\left[ \begin{matrix} 7 & 3 \\ 4 & 2 \end{matrix} \right] \), then 9I₂ - A = 

(a)

A^-1

(b)

\(\frac { { A }^{ -1 } }{ 2 } \)

(c)

3A^-1

(d)

2A^-1

If P = \(\left[ \begin{matrix} 1 & x & 0 \\ 1 & 3 & 0 \\ 2 & 4 & -2 \end{matrix} \right] \) is the adjoint of 3 × 3 matrix A and |A| = 4, then x is

(a)

15

(b)

12

(c)

14

(d)

11

If A, B and C are invertible matrices of some order, then which one of the following is not true?

(a)

adj A = |A|A^-1

(b)

adj(AB) = (adj A)(adj B)

(c)

det A^-1 = (det A)^-1

(d)

(ABC)^-1 = C^-1B^-1A^-1

If adj A = \(\left[ \begin{matrix} 2 & 3 \\ 4 & -1 \end{matrix} \right] \) and adj B = \(\left[ \begin{matrix} 1 & -2 \\ -3 & 1 \end{matrix} \right] \) then adj (AB) is

(a)

\(\left[ \begin{matrix} -7 & -1 \\ 7 & -9 \end{matrix} \right] \)

(b)

\(\left[ \begin{matrix} -6 & 5 \\ -2 & -10 \end{matrix} \right] \)

(c)

\(\left[ \begin{matrix} -7 & 7 \\ -1 & -9 \end{matrix} \right] \)

(d)

\(\left[ \begin{matrix} -6 & -2 \\ 5 & -10 \end{matrix} \right] \)

The system of linear equations x + y + z  = 6, x + 2y + 3z =14 and 2x + 5y + λz =μ (λ, μ \(\in \) R) is consistent with unique solution if _________

(a)

λ = 8

(b)

λ = 8, μ ≠ 36

(c)

λ ≠ 8

(d)

none

If the system of equations x + 2y - 3x = 2, (k + 3) z = 3, (2k + 1) y + z = 2 is inconsistent then k is ___________

(a)

-3, -\(\frac{1}{2}\)

(b)

-\(\frac{1}{2}\)

(c)

1

(d)

2

Cramer's rule is applicable only when ______

(a)

Δ ≠ 0

(b)

Δ = 0

(c)

Δ =0, Δ_x =0

(d)

Δ_x = Δ_y = Δ_z =0

In the system of equations with 3 unknowns, if Δ = 0, and one of Δ_x, Δ_y of Δ_z is non zero then the system is ______

(a)

Consistent

(b)

inconsistent

(c)

consistent with one parameter family of solutions

(d)

consistent with two parameter family of solutions

In a square matrix the minor M_ij and the co-factor A_ij of and element a_ij are related by _____

(a)

A_ij = -M_ij

(b)

A_ij = M_ij

(c)

A_ij = (-1)^i+j M_ij

(d)

A_ij =(-1)^i-j M_ij