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A matrix X has a+b rows and a+2 columns ...

A matrix `X` has `a+b` rows and `a+2` columns while the matrix `Y` has `b+1` rows and `a+3` columns. Both matrices `X Y` and `Y X` exist. Find `a` and `b` . Can you say `X Y` and `Y X` are of the same type? Are they equal.

A

3, 2

B

2, 3

C

2, 4

D

4, 3

Text Solution

Verified by Experts

The correct Answer is:
B
The order of a given matrices are `[X]_((a+b)xx(a+2))and [Y]_((b+1)xx(a+3))`
As [XY] and [YX] exist
`therefore a + 2 = b + 1 and a + 3 = a + b`
`rArr a + 3 = a + b`
`rArr b = 3`
Hence, a = 3 + 1 - 2 = 2
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