If A = $\left[\begin{array}{cc}3& 5\\ 2& 0\end{array}\right] \mathrm{and} \mathrm{B} = \left[\begin{array}{cc}1& 17\\ 0& - 10\end{array}\right]$, then $\left|\mathrm{AB}\right|$ is equal to

• 80

• 100

• - 110

• 92

The identity element in the group $\mathrm{M} = \left\{\left|\begin{array}{cc}\mathrm{x}& \mathrm{x}\\ \mathrm{x}& \mathrm{x}\end{array}\right|, \mathrm{x} \in \mathrm{R}; \mathrm{x} \ne 0\right\}$with respect to matrix multiplication is

• $\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$

• $\frac{1}{2}\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]$

• $\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$

• $\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$

In the group G = {1, 3, 7, 9} under multiplication modulo 10, the inverse of 3 is

• 1

• 3

• 7

• 9

If 2A + 3B = $\left[\begin{array}{ccc}2& - 1& 4\\ 3& 2& 5\end{array}\right] \mathrm{and} \mathrm{A} + 2\mathrm{B} = \left[\begin{array}{ccc}5& 0& 3\\ 1& 6& 2\end{array}\right]$, then B is

• $\left[\begin{array}{ccc}8& - 1& 2\\ - 1& 10& - 1\end{array}\right]$

• $\left[\begin{array}{ccc}8& 1& 2\\ - 1& 10& - 1\end{array}\right]$

• $\left[\begin{array}{ccc}8& 1& - 2\\ - 1& 10& - 1\end{array}\right]$

• $\left[\begin{array}{ccc}8& 1& 2\\ 1& 10& 1\end{array}\right]$

If O(A) = 2 x 3, O(B) = 3 x 2, and O(C) = 3 x 3, which one ofthe following is not defined?

• CB  + A'

• BAC

• C(A + B')'

• C(A + B')

206.

If A = $\left[\begin{array}{cc}1& - 3\\ 2& \mathrm{k}\end{array}\right]$ and A² - 4A + 10I = A, then k is equal to :

• 0

• - 4

• 4 and not 1

• 1 or 4

The value of $\left|\begin{array}{ccc}\mathrm{x} + \mathrm{y}& \mathrm{y} + \mathrm{z}& \mathrm{z} +\hspace{0.17em}\mathrm{x}\\ \mathrm{x}& \mathrm{y}& \mathrm{z}\\ \mathrm{x} - \mathrm{y}& \mathrm{y} - \mathrm{z}& \mathrm{z} - \mathrm{x}\end{array}\right|$ is equal to :

• 2(x + y + z)²

• 2(x + y + z)³

• (x + y + z)³

• 0

If A = $\left[\begin{array}{ccc}0& \mathrm{x}& 16\\ \mathrm{x}& 5& 7\\ 0& 9& \mathrm{x}\end{array}\right]$is singular, then the possible values of x are

• 0, 12, - 12

• 0, 1, - 1

• 0, 4, - 4

• 0, 5, - 5

The value of $\left|\begin{array}{ccc}\mathrm{x}& \mathrm{p}& \mathrm{q}\\ \mathrm{p}& \mathrm{x}& \mathrm{q}\\ \mathrm{p}& \mathrm{q}& \mathrm{x}\end{array}\right|$ is

• x(x - p)(x - q)

• (x - p)(x - q)(x + p + q)

• (p - q)(x - q)(x - p)

• pq(x - p)(x - q)

The characteristic roots of the matrix $\left[\begin{array}{ccc}1& 0& 0\\ 2& 3& 0\\ 4& 5& 6\end{array}\right]$ are

• 1, 3, 6

• 1, 2, 4

• 4, 5, 6

• 2, 4, 6