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For any matrix A and B other than identity matrix if AB=B and BA=A and (A+B)^3 = K (A+B), Find K ? |
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Answer» Step-by-step explanation: =>Here, AB=B & BA=A (AB).A=B.A & (BA).B=A.B A.(BA)=B.A & B.(AB)=A.B A.A=A & B.B=B A²=A & B²=B =>Now, (A+B)³ = K(A+B) (A+B)³-K(A+B) =0 (A+B)²-KI =0 (A²+2AB+B²)-KI =0 (A+2A+B) -KI =0 (3A+B)-KI=0 DIAG[3, 3, 3] + Diag[1, 1, 1] = Diag[K, K, K] Diag[4, 4, 4] = Diag[K, K, K] (4)Diag[1, 1, 1] = (K)Diag[1, 1, 1] => K=4 |
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