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# Solution - if  A=[[2,0,0],[0,2,0],[0,0,2]] then A^6 - HSC Science (Computer Science) 12th Board Exam - Mathematics and Statistics

#### Question

if  A=[[2,0,0],[0,2,0],[0,0,2]] then A6=  ......................

(a) 6A

(b) 12A

(c) 16A

(d) 32A

#### Solution

i. (d)

Given that

A=[[2,0,0],[0,2,0],[0,0,2]]

we can write

A=2[[1,0,0],[0,1,0],[0,0,1]]

Here 2 is scalar multiple

Terefore ,A=2 x I, where I= [[1,0,0],[0,1,0],[0,0,1]]

thus ,A^6={2[[1,0,0],[0,1,0],[0,0,1]]}^6

            =2^6xx[[1,0,0],[0,1,0],[0,0,1]]^6

=2^6xxI^6,

=26 x I,since I6=I

=2 5 x A [ A=2I]

=32A

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 1.1.1 | 2 marks

#### Reference Material

Solution for question: if  A=[[2,0,0],[0,2,0],[0,0,2]] then A^6 concept: null - Addition of Matrices. For the courses HSC Science (Computer Science), HSC Science (General) , HSC Arts, HSC Science (Electronics)
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