The amount of consideration paid or received in respect of both obtaining and losing control of subsidiaries or other businesses. [Refer: Total for all subsidiaries [member]]

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Name IAS
-Number 7
-IssueDate 2025-01-01
-Paragraph 40
-Subparagraph a
-URI https://taxonomy.ifrs.org/xifrs-link?type=IAS&num=7&code=ifrs-tx-2025-en-r&anchor=para_40_a&doctype=Standard
-URIDate 2025-03-27

+ Details

Name:	ifrs-full_ConsiderationPaidReceived
Namespace Prefix:	ifrs-full_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

- Definition

Line items represent concepts included in a table. These concepts are used to disclose reportable information associated with members defined in one or many axes of the table.

+ References

No definition available.

+ Details

Name:	ifrs-full_DisclosureOfSignificantInvestmentsInSubsidiariesLineItems
Namespace Prefix:	ifrs-full_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

The amount of deficit or surplus in a defined benefit plan, adjusted for any effect of limiting a net defined benefit asset to the asset ceiling. [Refer: Defined benefit plans [domain]]

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Name IAS
-Number 19
-IssueDate 2025-01-01
-Paragraph 140
-Subparagraph a
-URI https://taxonomy.ifrs.org/xifrs-link?type=IAS&num=19&code=ifrs-tx-2025-en-r&anchor=para_140_a&doctype=Standard
-URIDate 2025-03-27

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Note Effective 2027-01-01
-Name IFRS
-Number 19
-IssueDate 2025-01-01
-Paragraph 206
-Subparagraph a
-URI https://taxonomy.ifrs.org/xifrs-link?type=IFRS&num=19&code=ifrs-tx-2025-en-r&anchor=para_206_a&doctype=Standard
-URIDate 2025-03-27

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Note Effective 2027-01-01
-Name IFRS
-Number 19
-IssueDate 2025-01-01
-Paragraph 206
-Subparagraph a
-URI https://taxonomy.ifrs.org/xifrs-link?type=IFRS&num=19&code=ifrs-tx-2025-en-r&anchor=para_206_a&doctype=Standard
-URIDate 2025-03-27

+ Details

Name:	ifrs-full_LiabilityAssetOfDefinedBenefitPlans
Namespace Prefix:	ifrs-full_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

- Definition

The number of shares issued by the entity.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Note Expiry date 2027-01-01
-Name IAS
-Number 1
-IssueDate 2025-01-01
-Paragraph 106
-Subparagraph d
-URI https://taxonomy.ifrs.org/xifrs-link?type=IAS&num=1&code=ifrs-tx-2025-en-b&anchor=para_106_d&doctype=Standard
-URIDate 2025-03-27

+ Details

Name:	ifrs-full_NumberOfSharesIssued
Namespace Prefix:	ifrs-full_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

The nominal value per share.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Note Effective 2027-01-01
-Name IFRS
-Number 19
-IssueDate 2025-01-01
-Paragraph B10
-Subparagraph a
-Clause iii
-URI https://taxonomy.ifrs.org/xifrs-link?type=IFRS&num=19&code=ifrs-tx-2025-en-r&anchor=para_B10_a_iii&doctype=Appendix&subtype=B
-URIDate 2025-03-27

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Note Effective 2027-01-01
-Name IFRS
-Number 19
-IssueDate 2025-01-01
-Paragraph 160
-Subparagraph a
-Clause iii
-URI https://taxonomy.ifrs.org/xifrs-link?type=IFRS&num=19&code=ifrs-tx-2025-en-r&anchor=para_160_a_iii&doctype=Standard
-URIDate 2025-03-27

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Note Expiry date 2027-01-01
-Name IAS
-Number 1
-IssueDate 2025-01-01
-Paragraph 79
-Subparagraph a
-Clause iii
-URI https://taxonomy.ifrs.org/xifrs-link?type=IAS&num=1&code=ifrs-tx-2025-en-b&anchor=para_79_a_iii&doctype=Standard
-URIDate 2025-03-27

+ Details

Name:	ifrs-full_ParValuePerShare
Namespace Prefix:	ifrs-full_
Data Type:	dtr-2022:perShareItemType
Balance Type:	na
Period Type:	instant

- Definition

The proportion of ownership interest in a subsidiary attributable to the entity. [Refer: Total for all subsidiaries [member]]

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Name IAS
-Number 27
-IssueDate 2025-01-01
-Paragraph 17
-Subparagraph b
-Clause iii
-URI https://taxonomy.ifrs.org/xifrs-link?type=IAS&num=27&code=ifrs-tx-2025-en-r&anchor=para_17_b_iii&doctype=Standard
-URIDate 2025-03-27

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Name IAS
-Number 27
-IssueDate 2025-01-01
-Paragraph 16
-Subparagraph b
-Clause iii
-URI https://taxonomy.ifrs.org/xifrs-link?type=IAS&num=27&code=ifrs-tx-2025-en-r&anchor=para_16_b_iii&doctype=Standard
-URIDate 2025-03-27

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Name IFRS
-Number 12
-IssueDate 2025-01-01
-Paragraph 19B
-Subparagraph c
-URI https://taxonomy.ifrs.org/xifrs-link?type=IFRS&num=12&code=ifrs-tx-2025-en-r&anchor=para_19B_c&doctype=Standard
-URIDate 2025-03-27

+ Details

Name:	ifrs-full_ProportionOfOwnershipInterestInSubsidiary
Namespace Prefix:	ifrs-full_
Data Type:	dtr-2022:percentItemType
Balance Type:	na
Period Type:	duration

- Definition

New share issued to acquired non-controlling interests.

+ References

No definition available.

+ Details

Name:	math_NewShareIssuedToAcquiredNoncontrollingInterestsinShares
Namespace Prefix:	math_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Details

Name:	ifrs-full_CategoriesOfRelatedPartiesAxis=math_AntalphaMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

Overview of the Company (Details) - USD ($)	Feb. 28, 2023	Feb. 20, 2023	Nov. 28, 2022	Sep. 21, 2022	Mar. 31, 2023	Jun. 30, 2022
Overview of the Company [Line Items]
Equity interest			49.00%	100.00%
Consideration amount	$ 1	$ 1	$ 2,500,000	$ 1
Capital par value of shares (in Dollars per share)			$ 0.0001			$ 0.0001
Net deficit					$ 2,084,536
Antalpha [Member]
Overview of the Company [Line Items]
Equity interest			49.00%
Number of shares issued (in Shares)			2,500,000
Capital par value of shares (in Dollars per share)			$ 0.0001
Issuance of shares (in Shares)			2,500,000