if P×Q=I where P is a square matrix of order 2 and I is the identity matrix of order 2.Identify the relation of matrix P anta matrix
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Answer:
Q and P are inverses of each other.
Step-by-step explanation:
Given that P x Q = I
Order of P = 2 x 2
Order of I = 2 x 2
We know that multiplication of matrices is possible only when the no. of columns of first matrix = no. of rows of second.
And the resulting matrix is of the order m x n
where m is the no. of rows of first matrix and
n is the no. of columns of second.
Therefore, here as PQ is multiplied
No. of columns of P = no. of rows of Q = 2
As the order of I is 2 x 2
=> Therefore, no. of columns of Q = 2
Therefore, order of Q = 2 x 2
As PQ = I
Pre-multiplying P⁻¹ both sides
=> P⁻¹PQ = P⁻¹I
As P⁻¹P = PP⁻¹ = I
=> IQ = P⁻¹I
As IQ = QI = Q
=> Q = P⁻¹
Therefore, Q and P are inverses of each other.
P and Q being matrices of the same order
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