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प्रश्न
If M = `[(4,1),(-1,2)]`, show that 6M – M2 = 9I; where I is a 2 × 2 unit matrix.
उत्तर
M2 = `[(4, 1),(-1, 2)][(4, 1),(-1, 2)]`
= `[(4 xx 4 + 1 xx (-1), 4 xx 1 + 1 xx 2),(-1 xx 4 + 2 xx (-1), -1 xx 1 + 2 xx 2)]`
= `[(16 - 1,4 + 2),(-4 - 2, -1 + 4)]`
= `[(15, 6),(-6, 3)]`
6M – M2 = `6[(4, 1),(-1, 2)] - [(15, 6),(-6, 3)]`
= `[(24, 6),(-6,12)] - [(15,6),(-6,3)]`
= `[(24 - 15, 6 - 6),(-6 - (-6), 12 - 3)]`
= `[(9, 0),(0, 9)]`
= `9[(1, 0),(0, 1)]`
= 9I
Hence proved.
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