Question

what is the value of I3i3I,where i3 is identity matrix of order 3

Answer 1

hint : |aA| = a^n |A|
where n is the order of matrix

Answer 2

thereafter?

Answer 3

\[|3i_3|=3^3|i_3|=...?\]

Answer 4

note : \[|i_n|=1 \]
for any n.

Answer 5

so ? what value you get ?

Answer 6

i did'nt got it.sorry

Answer 7

when you take constant out of the determinant, it gets raised to an exponent of the order of matrix,
example , if |B| =5 and B is 5X5 matrix,then
\[|2B|=2^5|B|=2^5 \times 5\]
here, \[|3i_3|=3^3 |i_3|=...?\]
also since i is identity matrix, its determinant will be =1

Answer 8

okay.thx

Answer 9

so, what value did you get for that ?

Answer 10

3
3*3

Answer 11

\[|3i_3|=3^3 |i_3|=3^3 \times 1 = 27.\]

Answer 12

\[3^3\times3\]

Answer 13

but the determinant of identity matrix =1 , right ?
so , \[|i_3| =1 \]

Answer 14

thx

Answer 15

welcome ^_^