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Home > Matrix & Vector calculators > Power of a matrix example
4. Matrix Power example ( Enter your problem )
( Enter your problem )
  1. Definition and Examples
  2. Example-2
 		Other related methods
  1. Addition of two matrix
  2. Multiplication of two matrix
  3. Division of two matrix
  4. Power of a matrix
  5. Transpose of a matrix
  6. Determinant of a matrix
  7. Adjoint of a matrix
  8. Inverse of a matrix
  9. Prove that any two matrix expression is equal or not
  10. Minor of a matrix
  11. Cofactor of a matrix
  12. Trace of a matrix
1. Definition and Examples
(Previous example)		5. Transpose of a matrix
(Next method)

2. Example-2


1. Find `A^2` ...
`A=[[2,3],[0,5]]`

Solution:
`A^2`=`A×A`=
`2``3`
`0``5`
×
`2``3`
`0``5`


=
`2×2+3×0``2×3+3×5`
`0×2+5×0``0×3+5×5`


=
`4+0``6+15`
`0+0``0+25`


=
`4``21`
`0``25`


`A^2` = 
`2``3`
`0``5`
2
 = 
`4``21`
`0``25`
2. Find `A^3` ...
`A=[[2,3],[0,5]]`

Solution:
`A^2`=`A×A`=
`2``3`
`0``5`
×
`2``3`
`0``5`


=
`2×2+3×0``2×3+3×5`
`0×2+5×0``0×3+5×5`


=
`4+0``6+15`
`0+0``0+25`


=
`4``21`
`0``25`


`A^3`=`A^2×A`=
`4``21`
`0``25`
×
`2``3`
`0``5`


=
`4×2+21×0``4×3+21×5`
`0×2+25×0``0×3+25×5`


=
`8+0``12+105`
`0+0``0+125`


=
`8``117`
`0``125`


`A^3` = 
`2``3`
`0``5`
3
 = 
`8``117`
`0``125`


This material is intended as a summary. Use your textbook for detail explanation.
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1. Definition and Examples
(Previous example)		5. Transpose of a matrix
(Next method)


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