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  • Explain Solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and inverse of a Matrix Exercise very short answer type Question 6 maths textbook solution

Explain Solution for RD Sharma Maths Class 12 Chapter 6 Adjoint and inverse of a Matrix Exercise very short answer type Question 6 maths textbook solution

Answers (1)

VSQ-6

Answer: A must be invertible and \left | A \right |\neq 0

Given: A, B and C are non null square matrix of same order & AB=AC implies B = C

Hint : you must know about invertible and non-invertible matrix 

Solution : AB=AC can be write only when A is invertible\left | A \right |\neq 0

|A| \neq 0

A B=A C

Multiply both sides by A^{-1}

A^{-1} A B=A^{-1} A C

I B=I C

B=C

If Ais not invertible then A^{-1} does `nt exist then,

AB=AC

B=C

Hence, the condition of A is invertible or \left | A \right |\neq 0

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