Matrix Power Calculator

Your details

The number of rows and columns. Only square matrices can be raised to a power.
Integer exponent. Use 0 for the identity, positive for repeated multiplication, negative for inverse powers.
Result matrix A^n
[7, 10, 0] | [15, 22, 0] | [0, 0, 1]

The matrix raised to the given power, row by row.

Determinant of A^n4
Trace of A^n30
Determinant of A-2
Trace of A6
det(A)-2
det(A^n)4
tr(A)6
tr(A^n)30

A^2 computed for the 3x3 matrix.

  • A^2 was computed by repeated squaring (binary exponentiation), requiring at most 2 multiplications instead of 1.
  • The determinant property det(A^n) = det(A)^n is verified: det(A)=-2, det(A^n)=4.
  • The trace (sum of diagonal entries) of the result is 30.

Next stepTo solve a system A^n x = b, use the result matrix as the coefficient matrix and apply Gaussian elimination.

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