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If A=[-3 0 0-3] , find A^4 ....

If `A=[-3 0 0-3]` , find `A^4` .

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Given: `A=[(-3, 0),( 0,-3)]`
`A^2=[(-3, 0),( 0,-3)][(-3, 0),( 0,-3)]`
`A^2=[(9+0,0+0),(0+0,0+9)]`
`A^2=[(9,0),(0,9)]`
Then
`A^4=A^2.A^2=[(9,0),(0,9)][(9,0),(0,9)]`
`A^4=[(81+0,0+0),(0+0,0+81)]]`
`A^4=[(81,0),(0,81)]`
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RD SHARMA-ALGEBRA OF MATRICES-Solved Examples And Exercises
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  2. If A=[-1 0 0 0-1 0 0 0-1] , find A^3 .

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  3. If A=[-3 0 0-3] , find A^4 .

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  4. If [[x,2]][[3],[ 4]]=2, find x

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  5. If A=[a(i j)] is a 2xx2 matrix such that a(i j)=i+2j , write A .

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  14. If A is a skew-symmetric and n in N such that (A^n)^T=lambda\ A^n ...

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  16. If A is a skew-symmetric matrix and n is an even natural number,...

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