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Question
If A = `[(3, -4),(1, 1),(2, 0)]` and B = `[(2, 1, 2),(1, 2, 4)]`, then verify (BA)2 ≠ B2A2
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Solution
Here, B = `[(2, 1, 2),(1, 2, 4)]_(2 xx 3)` and A = `[(3, -4),(1, 1),(2, 0)]_(3 xx 2)`
∴ BA = `[(6 + 1 + 4, -8 + 1 + 0),(3 + 2 + 8, -4 + 2 + 0)]_(2 xx 2)`
⇒ BA = `[(11, -7),(13, -2)]`
L.H.S. (BA)2 = (BA) · (BA)
= `[(11, -7),(13, -2)][(11, -7),(13, -2)]`
⇒ `[(121 - 91, -77 + 14),(143 - 26, -91 + 4)]`
⇒ `[(30, -63),(117, -87)]`
R.H.S B2 = B · B
= `[(2, 1, 2),(1, 2, 4)]_(2 xx 3) * [(2, 1, 2),(1, 2, 4)]_(2 xx 3)`
Here, number of columns of first
i.e., 3 is not equal to the number of rows of second matrix i.e., 2.
So, B2 is not possible.
Similarly, A2 is also not possible.
Hence, (BA)2 · B2A2
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