feat(LinearAlgebra/Matrix): add Matrix.mul_eq_smul_one_symm

[dennj]

Summary

• Add Matrix.mul_eq_smul_one_symm: if M * N = c • 1 and det M ≠ 0, then N * M = c • 1
• A scalar generalisation of mul_eq_one_symm (the c = 1 case) to arbitrary scalars, requiring IsDomain and det M ≠ 0
• The proof uses the adjugate identity adjugate M * M = det M • 1 to derive det M • (N * M) = det M • (c • 1), then cancels det M via mul_left_cancel₀

Theorem imported from: https://github.com/Latinum-Agentic-Commerce/AlgebraicDesignTheory

[github-actions]

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[github-actions]

PR summary 4df4ffda6e

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

---

Declarations diff

+ mul_eq_smul_one_symm

You can run this locally as follows

## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>

The doc-module for scripts/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[eric-wieser]

Is a more general version of this true, building on top of #35676 ?