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Dear sir please find the answer of mentioned above as soon as possible...

swathi krishna , 5 Years ago
Grade 12
anser 1 Answers
Samyak Jain

Last Activity: 5 Years ago

Matrix X has (a + b) rows and (a + 2) columns and matrix Y has (b + 1) rows and (a + 3) columns.
\because XY exists, number of columns of X = number of rows of Y i.e.
    a + 2 = b +1  or  a = b – 1.
\because YX exists, number of columns of Y = number of rows of X i.e.
    a + 3 = a + b  or  b = 3.
\Rightarrow a = 3 – 1  or  a = 2.
This shows that X has 5 rows and 4 columns; has order 5x4. Y has 4 rows and 5 columns; has order 4x5.
We know that number of rows and columns of AB equals the number of rows of X and the number of columns of Y respectively if AB exists.
\therefore XY has order 5x5 and YX has order 4x4. XY and YX are square matrices and hence are of the same type.
But they aren’t equal as their orders are different.

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