State whether true or false: If A is a matrix and K is a constant, then \((KA)^T=KA^T\).

Q.1 (B) (i) State whether true or false: If A is a matrix and K is a constant, then \((KA)^T=KA^T\).

Doubtly Asked 28 Oct 2026 Board exam · March 2025 hsc 12th Save WhatsApp Report

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Answer: True

The \((i,j)\) element of \((KA)^T\) is the \((j,i)\) element of \(KA\), i.e. \(K a_{ji}\), which is the \((i,j)\) element of \(KA^T\). Hence \((KA)^T=KA^T\).

Doubtly AI · 28 Oct 2026 AI-verified · Oct 2026 Report

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State whether true or false: If A is a matrix and K is a constant, then \((KA)^T=KA^T\).

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