Multiply a matrix n times

I have a Matrix M, which should be multiplied N times. I know I have to use M^N simply. (^ without the point) but the elements of the matrix M are also vectors so I get the following error:

Error using ^

Inputs must be a scalar and a square matrix.

To compute elementwise POWER, use POWER (.^) instead.

The code is similar to below:

M11 = exp(1j.*k1.*d1) .* (cos(k2.*d2) + 0.5j.*((k2./k1)+(k1./k2)).*sin(k2.*d2));
M12 = exp(-1j.*k1.*d1) .* (0.5j.*(k2./k1)-(k1./k2).*sin(k2.*d2));
M21 = exp(1j.*k1.*d1) .* (-0.5j.*(k2./k1)-(k1./k2).*sin(k2.*d2));
M22 = exp(-1j.*k1.*d1) .* (cos(k2.*d2) - 0.5j.*((k2./k1)+(k1./k2)).*sin(k2.*d2));
M = [M11 M12;M21 M22];
TransMat = M ^ N;

In the above code, k1 and k2 are vectors. when k1 and k2 are only a number, the error will solve. I have to find M^N for different values of k1 or k2.

Thanks in advance

[Stephen23]

@Matthew Morrison: what is your definition of matrix power for a non-square matrix? Please show a reference for how this should be calculated.