# mpower, ^

Symbolic matrix power

## Syntax

``A^B``
``mpower(A,B)``

## Description

example

````A^B` computes `A` to the `B` power.```
````mpower(A,B)` is equivalent to `A^B`.```

## Examples

### Matrix Base and Scalar Exponent

Create a `2`-by-`2` matrix.

`A = sym('a%d%d', [2 2])`
```A = [ a11, a12] [ a21, a22]```

Find `A^2`.

`A^2`
```ans = [ a11^2 + a12*a21, a11*a12 + a12*a22] [ a11*a21 + a21*a22, a22^2 + a12*a21]```

### Scalar Base and Matrix Exponent

Create a `2`-by-`2` symbolic magic square.

`A = sym(magic(2))`
```A = [ 1, 3] [ 4, 2]```

Find πA.

`sym(pi)^A`
```ans = [ (3*pi^7 + 4)/(7*pi^2), (3*(pi^7 - 1))/(7*pi^2)] [ (4*(pi^7 - 1))/(7*pi^2), (4*pi^7 + 3)/(7*pi^2)]```

## Input Arguments

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Base, specified as a number or a symbolic number, scalar variable, function, matrix function, expression, square symbolic matrix variable, or square matrix of symbolic scalar variables. `A` and `B` must be one of the following:

• Both are scalars.

• `A` is a square matrix, and `B` is a scalar.

• `B` is a square matrix, and `A` is a scalar.

Exponent, specified as a number or a symbolic number, scalar variable, function, expression, or square matrix of symbolic scalar variables. `A` and `B` must be one of the following:

• Both are scalars.

• `A` is a square matrix, and `B` is a scalar.

• `B` is a square matrix, and `A` is a scalar.

## Version History

Introduced before R2006a

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