51
If $A$ and $B$ are matrices of order 3 and $|A|=5,|B|=3$, then $|3 A B|=27 \times 5 \times 3=405$.
A
TRUE
B
FALSE
52
If the value of a third order determinant is 12 , then the value of the determinant formed by replacing each element by its cofactor will be 144.
A
TRUE
B
FALSE
53
$\left|\begin{array}{lll}x+1 & x+2 & x+a \\ x+2 & x+3 & x+b \\ x+3 & x+4 & x+c\end{array}\right|=0$, where $a, b$ and $c$ are in AP.
A
TRUE
B
FALSE
54
$|\operatorname{adj} A|=|A|^2$, where $A$ is a square matrix of order two.
A
TRUE
B
FALSE
55
The determinant $\left|\begin{array}{lll}\sin A & \cos A & \sin A+\cos B \\ \sin B & \cos A & \sin B+\cos B \\ \sin C & \cos A & \sin C+\cos B\end{array}\right|$ is equal to zero.
A
TRUE
B
FALSE