The Inverse of the Matrix is Possible only for
The trick is after simplifying, Non-Singular Matrix is left. The method is simple: formula → substitution → calculation → answer.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
#matrix inverse
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If A=bmatrix x & 2 4 & 3 bmatrix and A ^-1=bmatrix 18 & -1 12 -1 6& 4 9 bmatrix , then find the value of x?
Applying the basic concept, solving fully: apply relevant formula, put numbers, compute. Result comes as 32 3. Easy verification shows it satisfies condition.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
If A = [ array*20c & - & array ] , then A-¹?
We know that we verify [ array*20c cos & - &cos array ] by full calculation: use standard identity, substitute, simplify step by step to reach [ array*20c cos & - &cos array ].
Ref: NCERT Mathematics Class XI — Trigonometry
If A = 13 ( array*20c 1&2&2 2&1&-2 -2&2&-1 array ) then (AAᵀ)-¹ = ?
Here's the idea in simple terms: complete solution: write formula, plug data, do arithmetic. Final value matches I. Simple and accurate.
Ref: NCERT Mathematics Class XI and XII
A is a scalar matrix with scalar k ≠ 0 of order 3. Then A-¹ is
From the definition, A=kI₃. Inverse formula (kI)⁻¹=(1/k)I. Because kI×(1/k)I=I₃. So answer (1/k)I. Full solution.
Ref: NCERT Mathematics Class XII — Matrices and Determinants
