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# C, 147 bytes

```c
float d(float**m,int r){if(r<2)return**m;int i=r,j;float s=0,*n[--r];for(;i--;s+=(i%2?-1:1)**m[i]*d(n,r))for(j=r;j--;)n[j]=m[j+(j>=i)]+1;return s;}
```

[Try it online!][TIO-ksv2632l]

Basically a C version of my example code. Takes an array of pointers and the size.

Prettified and commented version:

```c
float d(float **m, int r) {
	if(r < 2) return **m;  // Base case: 1x1 matrix

	int i = r, j;          // Variable initialization, i and j are counters
	float s = 0, *n[--r];  // s is the sum, n is the minor matrix

	for(; i--; s += (i % 2 ? -1 : 1) * *m[i] * d(n, r)) // Outer loop: loop over the rows of M.
	                                                    // After each iteration, add the term to the sum
		for(j = r; j--; )                           // Inner loop to fill in the minor matrix
			n[j] = m[j + (j >= i)] + 1;         // (j >= i) term skips over the ith row of M.
			                                    // Addition of 1 effectively removes the first element
	return s;
}
```

[Try it online!][TIO-ksv2hv64]

[C (gcc)]: https://gcc.gnu.org/
[TIO-ksv2hv64]: https://tio.run/##nVRNb5tAED3DrxjFsgQOOAHsfoQkVSv10EPVQ6P2QKxoC4u9LizWsk7dRv7rdWf4iB0HuW45jHeZeW/ePNYbu9M43mzSrGAaEqv@HQxyB4TUoGx4MA2RWgouwbdBcb1UkvIhwNkZvGMlhxjDBXgrD3KmlViZiECsgCtQDsyxsn0Q8YUpwb5lHOmFFiwTv5gWhcR2wGQCc2AKGYul1FyVplHrKZHq3IGBjFxXTerWJYgS9IxDuUSxst3lQhZqKyQtlBWCcN0QAadXYAnogw9vwPUANdswgEEeiQn@JhaqULZN5J@W2B6yolhcVBGKe9wTvyp@lFCk8HFoGvAfD5K/TYmcs3gGAlfN/CxJqgb4JgddtKOZRjXDnMwMYU6D2IfpP0jZaCeaVGQZev3cG8MwZDSfIG8ezeEUsMX1FQh7gmsv3CVsM7W08rtYlFs/hJ6RJ60lhnGsCUkiaHACesDTlMda3PPsJ56xHNnrr5kKVWrgGc@51KbRHL8yNNebnpBxtkw4XJY6EcVwdm2avYSnQnK4ef/55s63Vg7knkfBx@DTysdDfNseq1Wvd4fa77yIbHh4LIa1Q0W11rbIb4saHliHW6YBrJr0I6ezRTalC4V/i9Q6SbiGKOpPHehPJw60K8L3p7fypEu1g8cTx/FtO9wbM9gb0wt2UblP24C2AW2D4Ij5K5ajTKgadFYGbeVu73/wbLsMDtj31MKOXbepf/OocTuo3DbpMsuZkFZ1GTZnS/NSI8Ib4r10jmH/NqB3lLXNJxCfXo7xQ3ZA3IAwo@F4D4NyqszLDkzV3x3t9AkqzGhH2kF9B7LPRqipxw2ORqiE7YNHlBhTeNGRpSngFYXXRL02N7/jNGPTcuMueMKkFvHG/cqy7A8 "C (gcc) – Try It Online"

[TIO-ksv2632l]: https://tio.run/##lVJdb5swFH0uv@KqUSRM7CjYSbvNpXvaL1ilPVAURXzNCJzKUC1SlL8@5kugSTOUdX64@N57zv04OGZ5HLdtVm43DSRu9/W8iirdgCF7lbnmgROTNq9G27jEuAoMLeSRUgcL6umQMRPJbGtcqRiT9Sxw1ZR/Zf4Xn1hWqCIvcTU1hCCmCIwsLIzosIiCKixmbvEYKBLNfHnsBLU8tBOl4/I1SeGhbhK1nf98dJxJkmZKp/D07fvTmrs7CpXvo@HWcLxxTuDZuTlOt5tM1mb7a@2HEQSwfwPDgSIIujOA@ADq68BBnip5sOvTbzXpidlDX4yVJ3Nvk7SBMJzmFKZ5RGG4IX@aP@vbsampVd@uwwmRF2uKizV9cc6qOLoCXYGuEB/Yv6vyIRG6BqNIMSDPe/@HZqeruCLfewlHvHFR/6VRr7bo1HbwUVcbpV0Ce@emf1tNWjeW4c8XFBbWDPsPB2OYJc47Csfgyv7IEQoTyFnOVxccO06XuR/hdP3Z8qyP6DjLs9Guzncl@9cKx9KrnocrdINdkpeYWKG5G8niFvAJzWcsfXDa33FWbvK6ZS9pstGNilv2Y1OWfwA "C (gcc) – Try It Online"