How this calculator works
A positive integer power multiplies the matrix by itself that many times. The zero power gives the identity matrix. A negative power uses the inverse, so it requires a non-zero determinant. This calculator squares the matrix repeatedly, so even a power of 20 needs only a few matrix multiplications. Powers of a matrix obey the usual exponent rules A^m A^n = A^(m+n) and (A^m)^n = A^(mn).
Formula
A^k is the product of k copies of A; A^0 = I; A^(-k) = (A inverse)^k. det(A^k) = det(A)^k.
Worked example
The matrix with rows 1, 1 and 0, 1 squared is 1, 2; 0, 1, and its cube is 1, 3; 0, 1. The diagonal matrix with diagonal 2, 3 raised to the third power has diagonal 8, 27. Any invertible matrix raised to the power zero gives the identity.
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Frequently asked questions
Can I use a fractional power?
No. This calculator accepts whole-number powers only. Fractional powers would require a square root or a matrix logarithm, which is not defined for every matrix.
What happens with a negative power?
The calculator inverts the matrix first. A singular matrix has no inverse, so a negative power is rejected rather than producing a misleading result.
Does the power change the determinant?
Yes. The determinant of A^k is det(A)^k. A zero determinant stays zero for every positive power, and the zero power has determinant one.